Modern Australia is confident, independent, creative, cosmopolitan and incredibly varied as a tourist destination. Jonathan Bielski, the programming director at the Sydney Opera House, tells me that it all began with the creation of the Opera House in the 1970s, “which marked the end of our cultural cringe, so Australians wanted to hear their own accents on television and radio instead of BBC accents, and playwrights were writing with an Australian voice”.

Now, more than 30 years later, that cultural identity is fully forged, and visitors find theatre here on a par with London’s West End, modern art galleries that match those in Barcelona and Madrid in all the cities, and fine-dining restaurants that are the equal of any in the northern hemisphere. But where Australia really outstrips its tourism rivals is in the warmth, humour and friendliness of the people. There is nowhere that sporting travellers like to tour more than Australia – just ask the 40,000 Brits who followed the British and Irish Lions rugby union team around the country earlier this year. Equally, tourists looking for a big outdoor adventure happily take to Australia’s geographic extremities, because out there they are bound to find hospitality, helpfulness and a good dose of laconic humour to make any extreme adventure less arduous and more reassuring.

This year, I spent a month in Australia – my fifth trip there in 12 years – and when it ended, I found myself already planning my next trip. Here are some of the tips that I picked up on my five-city odyssey.

Brisbane

Long regarded as less cultured and civilised than Sydney and Melbourne, Brisbane has now acquired a state-of-the-art cultural centre and a handful of haute cuisine restaurants, and yet still maintains its small town feel.

*Best Hotel: Emporium, 1000 Ann Street, Fortitude Valley (from Dh1,052 for a Queen room, two people sharing). A modern, stylish, colourful, 102-suite boutique hotel, in a precinct that has more than 30 restaurants, cafes and cool shops. It has a rooftop terrace with heated saltwater lap pool, sauna and a small but well-equipped gym. An Italian restaurant - Tartufo - and a French patisserie - Belle Époque are attached to the hotel, and there is 24-hour in-suite dining.

*Best expensive restaurant/Best inexpensive restaurant: Esquire (expensive), 145 Eagle Street. Acclaimed owner/chef Ryan Squires offers a sophisticated but unpretentious degustation-driven restaurant that specialises in seafood. Squires worked as an estagiar at El Bulli and worked at Per Se and The French Laundry - hot credentials. It's the only restaurant in town with a three-hat award - the highest accolade in Australian cuisine. Sardine Tin (inexpensive), Little Stanley Street, South Bank. A cost-effective haven of European tapas, stylish company and outstanding service. "Small" courses cost 6 Australian dollars (Dh20) each and "large" cost 18 Australian dollars (Dh59). Real value for money.

*Best spa: Stephanies Spa Retreat, Sofitel Hotel, 249 Turbot Street. There are a variety of intensive spa experiences - a two-hour couples treatment for 274 Australian dollars (Dh901) per person, a two-and-a-half-hour massage, body wrap and milk bath at 395 Australian dollars (Dh1,299), and a three-hour Spice of Life treatment massage, mud and oils for 405 Australian dollars (Dh1,332), and many more.

*Best cultural experience: Gallery of Modern Art, Stanley Place, Cultural Precinct, South Bank. Brisbane's beautiful contemporary arts gallery is spread over three floors of exhibition space, and features exhibitions by international modern artists (Andy Warhol et al), but also has a significant indigenous collection. The front of the gallery is glass, so you have a constant view of the Brisbane River as you move from floor to floor.

*Best day trip out of city: The Noosa region is about 125km north of Brisbane, which is a 90-minute drive at most. Here, there are no skyscrapers or overcrowded beaches, and Noosa is set in a north-facing cove, so it’s protected from the elements. More rural and natural than the popular Gold Coast to the south, Noosa has a lovely national park; whales and their calves can be found here in considerable numbers in August and September, and Hastings Street, at the centre of the town, is lined with boutiques, coffee shops and good restaurants.

Sydney

Sydney is of the great cities of the world, with a population of four million, and, as the Opera House’s Jonathan Bielski says, a well-established confidence and a rich and sophisticated cultural offering. The restaurants aren’t bad either.

*Best Hotel: QT Sydney, 49 Market Street (Dh1,126 for a King room, two people sharing). Simply the coolest hotel in town, with 200 designer suites that successfully combine Gothic, art deco and Italianate features. Think Crosby Street Hotel with attitude. Housed in the historic Gowings and State theatre buildings, the public areas are fittingly dramatic, and the restaurant, Gowings Bar and Grill, is a European brasserie with Antipodean edge. SpaQ, the hotel's theatrical and highly rated spa, is also worth visiting.

*Best expensive restaurant/Best inexpensive restaurant: Marque (expensive), 355 Crown Street, Surry Hills. This is the award-winning restaurant of frequent chef-of-the-year Mark Best. Strongly influenced by new French cuisine, Best's brilliant molecular dishes are real food and not just melodramatic events. The 11-course degustation menu (165 Australian dollars [Dh543] per person) changes seasonally and is outstanding, while the three-course Friday lunch menu, at 45 Australian dollars (Dh148), is a real steal. Golden Century (inexpensive), 393-399 Sussex Street. The best bargain is this massive, 600-seater Cantonese restaurant that is a favourite of Sydney's top chefs. Expect to pay between 25 Australian dollars (Dh82) and 30 Australian dollars (Dh99) per head.

*Best spa: The Day Spa at The Langham, 89-113 Kent Street. A Sydney institution, and although there is strong competition from the SpaQ, the Langham (formerly The Observatory) still holds its own. But it's not cheap - 60-minute facials start at 190 Australian dollars (Dh625) and 60-minute massages start at 150 Australian dollars (Dh493).

*Best cultural experiences: There are two modern art galleries that I'd rate among the best in any capital city anywhere in the world. White Rabbit Gallery, 30 Balfour Street, Chippendale, has one of the world's most significant collections of contemporary Chinese art. Exhibitions change every six months. The Museum of Contemporary Art, 140 George Street, The Rocks, has ever-changing exhibitions and is a terrific space at the water's edge. A drive around the city guided by Richard Graham of My Sydney Detour offers a look at the great city's alternative culture, a world away from the Opera House and the Sydney Harbour Bridge. Graham is charming and extremely knowledgeable, and you're driven around in an iconic 1964 Holden EH, through suburbs that tourists don't usually visit. A three-hour Detour costs 207 Australian dollars (Dh682) per person.

*Best trip out of city: Actually you have to stay overnight to visit New South Wales’s increasingly popular district of Mudgee, which is Aboriginal for “nest in the hills”. It’s a three-and-a-half-hour drive or a 40-minute flight, but the drive is recommended, as you travel through the Blue Mountains. North of the town is the Putta Bucca wetlands, a waterbird paradise, and there are four national reserves in the region, as well as a number of historic villages that date back to Australia’s gold rush days.

Melbourne

The Economist Intelligence Unit has declared Melbourne one of the most expensive cities to live in. At the same time it’s rated as one of the world’s most liveable cities. Much to the chagrin of Sydneysiders, it’s also been dubbed the country’s cultural capital. Visitors will see that it’s a bit of all three.

*Best Hotel: Crown Towers, 8 Whiteman Street, Southbank (from Dh2,154 for a deluxe twin, maximum occupancy of four adults). Part of the Crown Entertainment Complex, which is casino, a mall of signature restaurants, and three very smart hotels on the city's Southbank. With spacious rooms, lavish bathrooms and very good service, it's as luxurious as you'll get in Melbourne.

*Best expensive restaurant/Best inexpensive restaurant: Vue de Monde (expensive), Level 55, Rialto, 525 Collins Street. This restaurant is very expensive, but it's spectacular, one of the hot spots in town both physically (it looks out over the city) and gastronomically. Shannon Bennett's modern Australian, with wild flourishes such as scrambled emu eggs and truffles, wallaby steak, and poached Pemberton marron (langoustine) with tarragon-spiked emulsion and salt dust, really is unusual. When you leave, you're given a goody bag of brioche and tea for tomorrow's breakfast, but for 250 Australian dollars (Dh822) a head, it's the least that you'd expect. Ombra Bar (inexpensive), 76 Bourke Street. An offshoot of Guy Grossi's famous Grossi Florentino restaurant, which is located next door, Ombra is based on northern Italian salumi bars, and is as cheap as Vue de Monde is expensive. It's also charming and serves delicious Italian food.

*Best spa: Spa at Crown Towers is a luxurious spa featuring private treatment rooms and couples suites, with a range of treatments, from a basic 30-minute relaxation massage (90 Australian dollars [Dh296]) through to hot-stone treatments (280 Australian dollars [Dh921]).

*Best cultural event: Melbourne International Comedy Festival, held every March/April, is one of the three largest comedy festivals in the world. It lasts for almost a month and has grown to be one of the country's major cultural events. Artists come from all over the world, and there are events large and small throughout the city.

*Best cultural experience: Hidden Secrets Lanes and Arcades Tour. The small, crowded lanes off the main streets host coffee shops, designer boutiques, chocolate and confectionery stores and all the other bits and pieces that give Melbourne its unique cultural verve. The two-and-a-half-hour walking tours are led by smart, enthusiastic guides, and are thoroughly recommended. The cost is 115 Australian dollars (Dh378) per person including lunch, or 95 Australian dollars (Dh312) per person without lunch.

*Best day trip out of city: Mornington Peninsula is an hour’s drive from the city, and is an area of fresh-food restaurants, casual cafes in coastal villages and seafood restaurants beside the sea. The emphasis is on locally grown produce. The peninsula is one of Victoria’s four biosphere reserves, and the only one with a resident population - around 130,000 people live there, most in the small towns on the western shore, and this number doubles with the summer visitors. There are also 20 golf courses.

Adelaide

This is the other Australian urban centre that is ranked as one of the world’s most liveable cities. A warm, Mediterranean climate, accessible rural retreats such as Adelaide Hills and Barossa Valley, and a population of 1.25 million easy-going South Australians all contribute. It certainly boasts one of the prettiest cricket grounds on earth.

*Best Hotel: Crowne Plaza Adelaide, 16 Hindmarsh Square (from Dh584, standard room based on two sharing). Perfectly located in the centre of the city, the Crowne Plaza is walking distance to the main attractions.* Best expensive restaurant/Best inexpensive restaurant: Auge (expensive), 22 Grote Street. A classy, stylish but unpretentious restaurant, Auge serves fresh Italian cuisine - the gnocchi with scallops, and the veal and mushroom risotto are recommended, as are the various steak dishes. There is an eight-course degustation menu for 129 Australian dollars (Dh424). It's the best Italian cuisine in Adelaide. Andre's Cucina and Polenta Bar (inexpensive), 94 Frome Street. This is a simple trattoria-style polenta bar. It's crowded and noisy, and costs between 40 Australian dollars (Dh132) to 50 Australian dollars (Dh165) a head.

*Best spa: Authenticity Spa Resort, 14-30 Waterport Road, Port Elliot, This is South Australia's original luxury spa resort, in the lovely coastal town of Port Elliot, just an hour's drive outside Adelaide. It's in an estate that has an idyllic botanical garden setting with wonderful cypress trees and an abundance of bird life. The day spa facilities are terrific.

*Best cultural event: Adelaide Fringe Festival is an annual arts festival during February and March that boasts 900 events, and attracts artists from all over the world in all forms of entertainment - Japanese jugglers, German vaudevillians, Canadian comic acrobats and so on.

*Best cultural experience: Take a drive to Adelaide Hills and visit The Cedars, the Australian landscape artist Sir Hans Heysen’s home and studio. The house, still owned by the Heysen family, is where Laurence Oliver and Vivien Leigh recited Shakespeare, Anna Pavlova danced and Dame Nellie Melba sang. It also has a fine collection of the artist’s work. A walking trail in the 60-hectare property direct visitors to the artist’s favourite painting sites.

* Best day trip out of city: Head to the Barossa for a country lunch. The picturesque rolling hills of the Barossa Ranges overlook a pretty patchwork of vineyards and picture-book villages, dotted with historic churches, stone buildings and 19th-century cottages.

Perth

The author Bill Bryson says that Perth is the most remote city on earth, and while not being strictly true, one gets the point. It’s certainly closer to many foreign capitals - Jakarta and Dili, East Timor - than it is to its own. This remoteness gives the city and Western Australia an other-world feel that makes it rather refreshing.

*Best Hotel: The Terrace Hotel, 237 St George's Terrace (from Dh990 for a deluxe suite based on two people sharing). Despite being a Best Western, the Terrace Hotel has considerable charm, not the least because it's housed in a listed building, St George's House, that dates back to the 19th century. It's a boutique property with only 15 suites, all fitted out with the latest technological niceties (flat- screen, digital television, in-room iPads, free Wi-Fi etc), and a staff who combine friendliness with efficiency. The restaurant is excellent and run by Shannon Wilson, who was once Sir Richard Branson's private chef, and the cuisine is modern, fresh Western Australian.

*Best expensive restaurant/Best inexpensive restaurant: Rockpool (expensive), Crown Perth, Great Eastern Highway, Burswood. The Western Australian version of Neil Perry's highly rated steakhouse sources directly from Australia's best beef producers. You'll pay 30 Australian dollars (Dh99) for charcoal roast king prawns, 55 Australian dollars (Dh181) for dry-aged, grass-fed, 250g fillet steak and 60 Australian dollars (Dh198) for rib-eye steak. Pricey but classy. Jamie's Italian (inexpensive), William Street. By contrast, Jamie Oliver's new WA restaurant features house-made pasta and antipasti boards, all for reasonable prices. A delicious orange, fennel and bocconcini salad costs 7.50 Australian dollars (Dh25), the fried squid dish 12 Australian dollars (Dh40), and a Sicilian sardine bruschetta 10.50 Australian dollars (Dh35) - all great value.

*Best spa: The Spa at The Richardson, 32 Richardson Street. In West Perth, this is an ESPA-designed facility that has an indoor, heated swimming pool, gym, sauna, poolside garden and all the treatments in the book. Signature treatments include Balinese massage (220 Australian dollars [Dh724]), the Age Defyer (250 Australian dollars [Dh822]), and chakra balancing with hot stones (275 Australian dollars [Dh904]).

*Best cultural experiences: The Indigenous Heritage Tour at Kings Park and the Botanic Gardens, where an Aboriginal guide takes visitors through Western Australia's unique plants, and explains how they're used both as bush food and traditional medicine. Also ancient dreamtime stories of the Nyoongar people are explained. The Western Australian Museum is well worth visiting, as it tells the story of the Aboriginal people, as well as displaying and explaining the unique meteorites, megafauna and dinosaurs that once inhabited prehistoric Western Australia. The State Theatre Centre/Heath Ledger Theatre features the 100-million Australian dollar, 575-seat theatre named after the late local hero, the actor Heath Ledger. It's the home of both the Black Swan and Perth Theatre companies, and a wide range of classical and avant-garde theatrical productions run through the year.

*Best day trip out of city: Just off Perth's west coast is the small island of Rottnest, or "Rotto" in the local vernacular. It's 25 minutes by ferry from Fremantle and 90 minutes from Perth. Take a bike or hire a bike there - no motorised vehicles are allowed on the island, which is a nature reserve. There are more than 60 beaches, and it's one of the best areas around Perth for snorkelling and scuba diving; there are a number of reefs and shipwrecks off the coast.