Floating in luxury aboard the Seven Seas Mariner

The panoramic view of coastlines and skylines as seen from the sea offers a unique perspective of a city, even if it is one you have visited before. Courtesy Regent Seven Seas Cruises

Max Davidson cruises through the history and beauty of the Mediterranean and Adriatic coasts.

Athens, Ephesus, Santorini, Ancient Olympia, Corfu, Dubrovnik, Venice ... To visit them all in a week in the most luxurious of surroundings, without spending half the time in airport terminals, feels like a miracle of 21st-century living. As the Seven Seas Mariner sails out of Piraeus, the port of Athens, with the sun setting behind us and the gentlest of breezes on our faces, we feel a sense of real excitement, as if journeying into the unknown.

Our fellow passengers - predominantly American, but with a good mix of other nationalities - are far more diverse than we had been expecting. Cruising is often associated with the over-sixties, happy to take life in the slow lane, but here there is everything from honeymooners to families with small children. And with 750 passengers and 500 crew and staff, our floating village feels just the right size, not too big or too small.

At the observation lounge on the top deck, we chat to a delightful couple from Denver, Colorado, while a pianist plays A Nightingale Sang in Berkeley Square. Out on deck, a man is thrashing golf balls into a net, while his wife power-walks around in circuits listening to her iPod. There is a queue for ice creams beside the swimming pool.

Our suite is enormous, bigger than our living room at home, and there is even a smiling butler, which we certainly don't have at home. The trappings of luxury are all around us. Cruise ship food can be mediocre, particularly on all-inclusive cruises, where bland buffets are the norm. But the Mariner's four restaurants all offer fine dining, with cuisine ranging from French and Italian to American steakhouse. We could be in a top city hotel as white-jacketed waiters lift silver domes to reveal immaculately presented fish dishes - except that, in a top city hotel, we would not be gliding across the Aegean at sunset, marvelling at the view.

On-board entertainment ranges from tea-time quizzes to late-night dancing, lectures about Ancient Greece to roulette and baccarat, auctions of fine art to Beatles tribute nights. It is all enormous fun, nobody takes life too seriously, new friendships are struck up every day and you could have a ball without leaving the boat.

But, of course, with our star-studded itinerary, the urge to leave the boat is irresistible. The destinations on the cruise span thousands of years of history and some of the most iconic locations in the world, from the Acropolis in Athens to St Mark's Square in Venice.

The highlight for us, against very stiff competition indeed, is Santorini, probably the most photographed of all the Greek islands. It is situated on top of a large volcanic caldera, formed by a massive eruption around 1500 BC.

As the ship anchors in the circular bay and tenders arrive to take us ashore, we peer blinking up the sheer cliff-faces, more than 300 metres high, at the communities perched vertiginously on the rim of the caldera.

Access to the capital, Fira, is by cable car or donkey. "Donkey," says my fun-loving wife. "Cable car," I insist. It is a steep climb, there is more of me than there used to be and I don't want to be accused of cruelty to animals. But the view from the top is even more spectacular than the view from the bottom.

In the midday sun, the bright blue roofs of the white-washed houses vie with the blue waters of the bay below. Bougainvillea cascades over balconies. Cats sleep in the shadow of old churches. A sea breeze gusts the windmills. All the poetry of the Greek islands is caught in a series of timeless vignettes.

Some of the other destinations on the cruise, such as Ephesus and Ancient Olympia, are inland and require short bus transfers; but there is no sense of inconvenience as we admire the scenery, take in the pomegranate trees and the olive groves and the tall pines, then explore the famous archaeological sites.

Ephesus, in Turkey, is particularly splendid. It used to be the third largest city of the Ancient World, after Rome and Alexandria, and although only a fraction of the city has been excavated, you can get a clear sense of what it must have been like in its pomp. The great Temple of Artemis, one of the Seven Wonders of the Ancient World, is no more, alas - you need to look at the reconstruction in the museum to get a sense of its scale. But you can still see the remnants of the 44,000-seat theatre, where gladiatorial combats took place, and the quite stunning facade of the library, which would grace a cathedral.

Ancient Olympia, in the Peloponnese, feels more intimate, a jumble of ruined temples and other buildings in a tranquil hillside setting beside a stream. As you wander through the site, lulled by the sound of cicadas, it is hard to imagine that for more than a thousand years athletes travelled here from all over the Aegean to take part in the Olympic Games, held every four years from 776 BC.

The dusty stadium where the athletes competed feels touchingly diminutive compared with the facilities at the Olympic Park in London, but it is good to be here, good to remember the ghosts of the past, good to stand on the site where the sacred Olympic flame was lit at the start of the games - and is still lit to this day.

Our last port of call in Greece is Corfu, where we stroll the narrow streets of the old town, do some light shopping, visit the old Venetian castle, then have lunch overlooking the gracious tree-lined esplanade. Then it is on to Dubrovnik and Venice and the journey's end.

There cannot be many prettier spots in the whole Mediterranean than Dubrovnik in Croatia, tucked into the Adriatic coast in the lee of a small wooded island. Its old walls are still intact and you can walk around them in less than an hour, admiring the beautiful old buildings with their red-tiled roofs and the blue sea beyond. The city is car-free, which gives it a relaxed, festive air. From soaring baroque churches to bustling fruit-and-vegetable markets to shops selling stylish modern jewellery, it is a walker's paradise with something new around every corner and little side alleys holding out the promise of a funky shop or cafe.

And finally to Venice, which needs no introduction. We have been there many times before, but are unprepared for the sheer visual delight of arriving in the city by boat: passing the Lido, then inching towards St Mark's and the Grand Canal, with a panoramic view of the famous skyline and the lagoon beyond.

Our ship moors a little way from the city centre - it wouldn't do to drop anchor next to the Bridge of Sighs - but here we are and here, as at every port of call, is the printed menu of optional excursions, all mouth-watering and all complimentary.

Will it be "Venetian Palaces", "The Grand Canal and the Guggenheim Collection", "Hidden Treasures of Venice", "The Islands of Murano and Burano" or "Venice by Gondola"? We plump for the gondola, being incurable romantics, but quite frankly, we could be taken on a tour of Venetian shoe-shops and still feel as if we were walking on air. On this most stylish of cruises, the sense of being pampered 24/7 and treated like royalty on tour has been exhilarating and heart-warming.