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The Thinking Traveller’s Iremia villa on Antipaxos, one of the less-crowded Greek islands

 The Thinking Traveller

Antipaxos, Ionian Islands

Less than 30 people live on Antipaxos, the three-mile large islet one mile off the coast of Paxos. But every summer day hundreds of visitors to Paxos make the 15-minute boat trip to spend a few hours swimming in the turquoise seas off of Antipaxos’s three main beaches, pebbly Mesovrika and Voutoumi or white-sand Vrika. You can swim or snorkel in the crystal-clear waters—or head to the nearby, even smaller islet of Daskalia to scuba dive, hike the hills, and eat in one of the island’s four simple, delicious tavernas: Spiros Taverna or Vrika Beach Taverna on Vrika beach, Voutoumi Beach Bar and Restaurant on Voutoumi beach, or Bella Vista, on the hill above Voutoumi beach. The tavernas only serve lunch (which, this being Greece, can go as late as sunset)—as there isn’t much of a dinner crowd given the lack of hotels on the island. There are, however, some villa retreats if you’d like to feel like you have the island to yourself after the beachcombers head home. You can find posh options on U.K.-based sites such as Condé Nast Traveler specialist The Thinking Traveller and Ionian Villas, and simpler homes on Airbnb and Vrbo. Just remember, if you book one, you’ll have to bring groceries from Paxos.

A beach in Meganissi

 Five Star Greece

Meganissi, Ionian Islands

The name means “Big Island,” but don’t be fooled—this nine-mile isle is just the largest of the 10 islets dotted along the coast of Lefkada in the Ionian sea. It’s a half-hour ferry ride (five nautical miles) from the rowdy port town of Nidri on Lefkada, but it’s also billionaire adjacent; Meganissi’s neighboring island is Skorpios, once owned by Aristotle Onassis, now the property of a Russian billionaire who is rumored to be redeveloping it into an ultra-high-end resort. On Meganissi, you can sun on white stone beaches (not, one hopes, being snapped topless by paparazzi on a boat as Jacqueline Onassis once was), scuba dive, explore the three main villages (Spartochori, Vathi, and Katomeri), or rent a boat and sail to secluded coves or sea caves so large they’re said to have provided shelter for Greek submarines during World War II. There are a few small hotels but this is largely villa (or yacht) country. Find one through Five Star Greece, The Thinking Traveller, and British outfits such as CV Villas, or more basic accommodation through Vrbo.

Kastos

 Jan Mach/Getty

Kastos, Ionian Islands

If you’re looking for an island to call (practically) your own, we’ve got the spot for you. A 50-minute, once-daily ferry ride from the port of Mitikas on the mainland, Kastos is an ideal place to get away from it all. At just four miles long, the smallest inhabited island in the Ionian sea is home to about 50 permanent residents and dozens of cobalt bays where sailors drop anchor in summer to snorkel, scuba dive, or explore sea caverns such as Fokotrypa (named for the seals that sometimes hide there). Join your fellow adventurers to enjoy a meal in one of the harbor’s four tavernas or watch the sunset from one of the bars. Or, go your own way and seek out one of the isolated beaches on Kastos’s east coast to swim in splendid isolation. There are one or two apartments to rent by owner but by far the most luxurious place to stay is the Thinking Traveller’s Villa Gaia, a hilltop hideaway which comes with an infinity pool and a 4X4 for puttering around (although you can also walk down the tree-covered hilltop to the beach below).

Acantha Boutique Hotel

 Acantha Boutique Hotel

Ereikoussa, Ionian Islands

The northernmost Ionian island, Ereikoussa is one of Corfu’s three satellite islands, known collectively as the Diapondia. Only eight miles and a 1- to 2.5-hour ferry ride or 35-minute private boat ride from Corfu, Ereikoussa is ringed by two main sandy beaches, Porto and Bragini. The interior of the five-mile islet is fragrant with cypress and olive trees, and full of wild lilies in spring and the purple-heather called reiki, which gives the island its name, in fall. An undiscovered paradise, Ereikoussa has a few small hotels, including the Erikousa Hotel and the Acantha Boutique Hotel, an adults-only property, both short walks from Porto beach; and a handful of rental homes from Hip Away Villas or Vrbo. Most of the vacationers on Ereikoussa are descendants of the islanders who emigrated to America and return to spend the summer swimming and scuba diving in the surf or biking and hiking on the turf. If you crave more activity than that, take a day trip to neighboring Othonoi and hike to the lighthouse, and visit the postcard-perfect village of Vitzsentziatika to take in the view of both Italy and Albania in the distance.

A cove on Marathi island

 Getty

Marathi, Dodecanese

Private yachts from Patmos and the occasional day trip boats from Lipsi or Leros sail to Marathi so the sun-seekers aboard can swim in the crystal-clear waters surrounding the island. But once they leave, the only souls left on the isolated hideaway are the dozen hardy people who live here (and dwindle down to three in winter) and the adventurers who find refuge in the rooms they rent. All of the island’s action, such as it is, is centered on Marathi beach. That’s where you’ll find three tavernas that offer rooms, including Pantelis Marathi, run by the Emilianos family, who came to the island in 1977 and never left. The same clan also manages simple, ocean-view homes for rent, bakes the bread served in their taverna, and sources the ingredients chef Katina cooks from nearby islets: tomatoes from Leros, dairy from Arki, fish from the sea. There’s one blue-domed church dedicated to Agios Nikolaos, the patron saint of sailors, lots of birds and goats, and nothing to do but read and relax, making this the ideal spot for philosophers, romantics, fugitives, or anyone looking to get lost for a while. (Just make sure to leave a few days buffer between Marathi and your flight home; if it’s windy, the excursion boats you’ll take to go back and forth to one of the larger, neighboring islands like Leros, Lipsi, and Patmos won’t sail.)

The Windmill hotel on Kimolos

 Aria hotels

Kimolos, Cyclades

Not quite 14 square miles large, Kimolos is less than a mile from its big sister island, Milos, and the distance between them can be bridged with an hour-long ferry ride or half-hour hydrofoil. That means the seas around it are every bit as stunning, boasting the same—and arguably, even bolder—cobalt-glass and emerald-green hues. There’s also a whitewashed Cycladic village at its peak (called Chorio, which means “village” in Greek), and a top-notch taverna—To Kyma—on the sandy beach next to its port. Royals of the noble and Hollywood kind have been known to dock their yachts in the natural harbor at Poliegos, the neighboring deserted islet. Should you find yourself without a boat of your own, you can book options from a windmill to a beach house through