There’s a full moon rising over the sleepy Ionian island of Kythira, throwing silvery light over the clifftop castle, Chora Kythira. My partner, David, and I are sitting in a beachfront taverna, toes in the sand, tucking into fresh sea bream, Greek salad and a carafe of chilled rose, gazing out at the dark sea. All around us, the lively chatter is in Greek. This is an island the locals like to keep for themselves.

Kythira is just one of several overnights in port where we eat ashore, which is the general idea of this cruise. I can’t think why other lines haven’t caught onto the idea of offering half board in the Greek islands, where whiling away happy evenings and long, restina-soaked lunches in beachfront tavernas is all part of the experience. Variety Cruises, though, does this on most of its Greek voyages. On this week-long odyssey around the Peloponnese and the Cyclades, we start the day on board with Greek yoghurt and chopped fruit and nuts, drizzled with fragrant local honey, but for either lunch or dinner, we’re on our own. For David and I, this varies from a full pig-out of swordfish, souvlaki, salads and dips in a vine-shaded alley in Syros to a picnic of cheese pies, still warm from the village bakery, on the beach in Kia.

Harmony G, our home for the week, really is a very tiny ship, taking just 42. The ship’s petite size means you’re more likely to be tied up in smart marinas, or alongside at local town jetties, than sandwiched in between megaships in more commercial ports. The experience is certainly akin to that of a private yacht. You get a comfortable cabin, excursions and superb food, but can forget about waterslides, spas and Broadway shows. Instead, there’s just a sundeck, restaurant, a bar and a swimming platform. Greece itself is the entertainment and the Aegean our swimming pool.

In fact, swimming off the back of the ship is for many of us a highlight of each day. Captain Theo picks a good spot to drop anchor and the whole passenger contingent, aged from 14 to 84, plunges into the inky blue water for a cooling dip. The more competitive among us swim laps around the ship, while others are content to bob around or don mask and snorkel to dive down into the dappled aquamarine. These swimming stops, as well as the communal meals in the small restaurant (no tables for two here) are a time to bond with our fellow passengers: French, Germans, Americans, Australians and Brits.

Small ships don’t have to follow rigid schedules, which is just as well, as it was too windy for the planned run to Mykonos, our first port. Instead, Captain Theo said we would do the itinerary in reverse, so we pitched up at the gorgeous old town of Nafplion, where graceful Venetian houses line streets of gleaming marble and a Greek dancing festival was in full swing.

Day two and the wind had dropped, which made the hike up to the ruined citadel on the fortified peninsula of Monemvasia hard work, the air, scented with wild herbs, shimmering in the heat. The view, though, was worth it, over the terracotta rooftops of the tiny town and the glittering sea.

Although the week included star attractions like Mykonos, Crete and Santorini, it was the less touristy places like Monemvasia and Kythira that I really loved. Having said that, if you’re new to Greece and want to sightsee, there is a programme of reasonably priced excursions, ranging in price from €57 for a half day to the archaeological site of Mycenae to €85 for a trip to the Palace of Knossos in Crete. We did this one and were impressed by both the tour and the lunch that followed, in a village taverna – zucchini balls, spiced sausages, salads and a kind of Cretan bruschetta, although the village wine left something to be desired.

For all the culinary discoveries ashore, the food on board was outstanding: fresh salads with handfuls of fresh herbs, barbecued meats and plenty of seafood. One day, the crew served ouzo and grilled octopus on deck before dinner while on another, a succulent grouper, big enough to feed all of us, was wheeled out for lunch.

After feasts like this, I’d just flop on deck for the afternoon, watching the sun dance on the navy water as we sailed past scrub-covered islands studded with white houses, goat tracks zig-zagging down to rocky coves. My kind of paradise.