While everyone else fights for santorini sunsets and Mykonos beach clubs, one family discovered that Greece's most rewarding island might be the one that's genuinely hard to reach. Ithaca — a sliver of green in the Ionian Sea, just 18 miles end to end — is famed in legend as Odysseus's homeland, and it turns out the mythology is the least of its charms.

Getting there is a mini-odyssey in itself: a flight to Kefalonia, a taxi across that island to the port of Sami, a 30-minute sea taxi, then a 40-minute drive. The payoff? Bay views that prompted even a hard-to-impress teenager to say "wow". The writer's family based themselves in an apartment above Kioni, a pretty harbour village with a handful of tavernas, bars and shops — no pool needed when the Ionian is on your doorstep.

The beaches are pebbly rather than sandy, and mostly small coves reached on foot down cypress-flanked paths. One local favourite sits cheerfully beside the cemetery, with a kantina dishing up calamari, souvlaki and carafes of house wine. Because Ithaca takes effort to reach, there are no tourist hordes even in August, and tables at harbour restaurants — serving octopus, moussaka, kleftiko and wood-fired goat — are findable without booking.

The smart move here is to rent a boat instead of a car. A speedboat costs around €150 for the day, and with a paper map (and the boat owner tracking you by GPS) you can hop between deep blue inlets the writer compares favourably to the Caribbean, swim to beaches you'll have entirely to yourself, and — if you misjudge the currents like this family did — accidentally breakfast on neighbouring Kefalonia. They also spotted flying fish and a large turtle along the way.

There's substance beyond the swimming. Kefalonia has lately claimed the Odysseus birthright, but British author Jane Cochrane's book Walking in the Footsteps of Odysseus makes a firm case for Ithaca, while also charting how the devastating 1953 earthquake destroyed more than 70% of the island's buildings and scattered generations of local families. Reading it before a wander into Kioni's backstreet shops adds a layer of local colour you won't get on a fly-and-flop package.

Who is Ithaca for? Families with teens who want some independence, couples who like their tavernas without a shot-bar strip, and anyone who'd rather helm a speedboat than queue for a sun lounger. Simpson Travel has a week at the Kyparissi Suites from £865 per person including flights, transfers, hire car and Atol protection. Book early — the family found nearly everything popular already full by the end of May.