It starts with a faint tremor that I feel in the soles of my feet. Engines rumble and the horizon shifts subtly on its axis. I rush to the ship's railings and see ropes cast off and the gap to the quay widening. This is the most exhilarating moment in cruising, which I never want to miss. The inconveniences of travel have been navigated and stowed away with my suitcase. Everything is easy from now on, and adventure awaits over the watery horizon.

Sailing out of Athens is particularly thrilling. Over thousands of years others, from Odysseus to Herodotus, have enjoyed this same moment, though perhaps minus the cocktail. Athens rises from the Attic Plain in the orange haze of the late-afternoon sun. The Acropolis is a stubby outcrop crowned by temple columns that are the exclamation marks of a culture that has influenced the world.

Azamara Pursuit picks its elegant way between container ships into the inky-blue Aegean Sea. The ship is taking me on a 10-night Greece Intensive cruise that finishes in Venice and visits Kotor in Montenegro, but which concentrates on the Greek islands.

There are few better places to sail. The Aegean has been crosshatched by the wakes of ancient Greeks and Romans, Byzantines and Ottomans, crusaders and invading sun seekers. It has history and hedonism. It stirs the intellect, yet tempts with salty swims and chatter-filled cafes.

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Tourists and tourist boats in the famous Navagio Bay on Greece's Zakynthos island.

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Each island has its distinct character, but all are close enough that passengers are off the ship all day and transported by night. Next morning, our first port of call is Spetses, which is almost ignored by international tourists. Wealthy Athenians come here to escape to bougainvillea-draped villas on pine-scented hillsides. The pines have supplied ships' masts since ancient times. In the harbour boatyard, workers are still making wooden fishing boats with traditional tools. Wrinkled men sit in the sun playing backgammon. The port town is stately with neoclassical buildings. Cars are banned and horse carriages clip clop along the waterfront.

Spetses has no particular sights, but everything that makes Greece magical. A rugged landscape of rocks, hills and scented forest, a tumble of whitewashed houses, shadowy chapels hung with icons and scented with candle wax and polish. Blinding light and blue sky, the blue domes of churches, the silvery shiver of olive trees, the happy splatter of red and orange beach parasols. This is a delicious nothing-to-do cruise day. I meander along the waterfront, hike up to a ruin, devour the first of many baklavas accompanied by thimblefuls of thick Greek coffee.

Next day is quite another experience. The whole world has discovered Mykonos: sun-pink Germans, posturing Chinese photo models, raucous Englishmen, jet-setting party people. Parts of Mykonos town's narrow streets are log-jammed with tourists, their cubic whitewashed architecture hidden under a veneer of hanging T-shirts and postcard racks. Still, it's hard not to be seduced by the whitewashed charm, and a short wander up the hill takes me to silent streets and a dilapidated windmill from which to admire a calendar-worthy island view.

That afternoon I take an Azamara excursion to Delos. This little island on which the Cyclades archipelago centres was considered the birthplace of Apollo and Artemis, and in ancient Greek times was the location of a prominent sacred and commercial town. Its ruins are scattered with mosaics, headless statues and toppled pillars. Marble lions have stood here since the second century BC, and are a brooding presence in a rocky, sun-beaten landscape.

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It's hard not to be seduced by the whitewashed charm of Mykonos.

I squint towards Mykonos, modern-day temple to tourism, and wonder what will remain in another millennium. Greece does this to travellers. It makes you philosophise and contemplate the vagaries of history, even while it distracts you with all the shameless pleasures of 21st-century tourism: beach clubs and coffeehouses, Insta-views and sunsets, warm waters and inflatable flamingo floats.

As we sail onwards, I find Azamara Pursuit caters to the split personality, too. It offers thoughtful seminars and enrichment lectures, and a ship's library of Georgian-style elegance and considerable literary heft. It's an elegant ship of understated appeal almost as minimalist as the Aegean landscapes, yet is never short of indulgences. I like the pool-side hot tubs, the White Night evening barbecue on deck, the properly made coffee from Mosaic Caf and the foie gras with fig jam from Aqualina restaurant.

As we sail onwards, each island is unexpectedly different. At Rhodes, we sail in under crusader battlements to spend the day exploring one of Europe's best-preserved medieval fortified cities. In Crete, there are wild landscapes and village life, and the crumbling ruins of Ottoman castles. By day seven we've arrived in the Ionian Sea to anchor off Zakynthos, where limestone cliffs plunge into peacock seas and a shore excursion takes me into a rural world of folk tales and saintly miracles.

Azamara Pursuit is ideal for these petite ports. The ship carries 702 passengers and, though it has space and a full range of amenities, is compact enough to visit smaller destinations. It's an attractive ship but caters to those who like to be off it and exploring for most of the day, and sometimes into the evening, too. Azamara Club Cruises is destination-focused, lingering in ports and providing an impressive range of shore excursions. A choice of 10 in Rhodes, nine in Zakynthos and nine in Mykonos, ranging from mosaic-making to a monastery visit, a four-wheel-drive adventure to a culinary walk.

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Azamara Pursuit is an elegant ship of understated appeal.

I like the structure of the shore excursions, and the time they leave for exploration on my own. In Corfu, a morning visit to Achilleion Palace still leaves the entire afternoon free for Corfu old town, the jumbled alleys of which are edged with a fine, arcaded Esplanade and parks, all overlooked by a whopping Venetian-era fortress. This is a lovely place of statues, pastel-painted houses and bakeries hot with the smell of nut biscuits dipped in honey. Tourists surge, but in the Church of St Spyridon local widows in black queue beneath a flamboyantly painted ceiling to kiss the patron saint's silver coffin.

We sail away between the Corfiot and Albanian coastlines. The pie-crust roofs and fortifications of Corfu are left in our wake. Albanian towns are an enigma to starboard, glowing like the promised land in the last of the Mediterranean sun. That could be a place to visit one day, I think as I pace the decks. A good cruise leaves you wanting more, as the travel muse sings across the silvery sea.

FIVE SIGHTS BEYOND THE PORTSKNOSSOS PALACE

From Cretan port Agios Nikolaos, a shore excursion takes you to these 1250BC Minoan ruins, one of the world's most famous archaeological sites. The nearby Museum of Heraklion's artefacts highlight the sophistication of this ancient civilisation. Seeheraklion.gr

REMOTE ZAKYNTHOS

To prove there are still untouched spots in Greece, a 4WD tour winds into the rugged Vrachionas Mountains and onwards to remote inland villages Anafonitria and Volimes. There's also a stop above Shipwreck Beach, one of Greece's most stunningly blue coves. Seevisitgreece.gr

LINDOS

AnAzamara excursion across Rhodes island goes to the lace-making town of Lindos, whose cubic houses are scattered like white dice below an acropolis of ancient remains and Venetian fortifications. The combination of temple ruins and landscape is sublime. Seerodosisland.gr

ELIA BEACH

For your hedonistic moment, head to one of Mykonos' most magnificent beaches, lapped by emerald-tinted waters and embraced by craggy cliffs. Rent a sun lounge and thatched parasol and enjoy a day of sun-soaking and swimming among Europe's buffed and beautiful. Seemykonos.gr

ACHILLEION PALACE

This odd but attractive neoclassical mansion in Corfu was built in 1890 for melancholy Empress Elizabeth (Sissi) of Austria and later owned by Kaiser Wilhelm II. The curator takes you around the interior and statue-studded gardens with their sweeping terrace views over Corfu. Seeachillion-corfu.gr

TRIP NOTESMORE

visitgreece.gr

CRUISE

Azamara offers three Greece Intensive Voyage itineraries in 2020 that sail between Athens and Venice (or the reverse). They all differ slightly from each other and the one described here. Prices from US$2667 a person, twin share. azamara.com

Brian Johnston travelled as a guest of Azamara.

A return trip for one passenger in economy class flying from Auckland to Athenswould generate 3.2 tonnes CO2. To offset your carbon emissions head toairnewzealand.co.nz/sustainability-customer-carbon-offset.

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An Aegean cruise aboard Azamara Pursuit proves there are few better places to sail - Stuff.co.nz