Greece is a country of water and sky as much as rock and soil. This elemental interfingering – bay, mountain, cape, isthmus – always leaves the traveller with a sense of elation. When you add Greece’s unmatched and extended summer weather, with six months of pink dawns, white noons and lacquered evenings, it’s hard to imagine a better spot to lance the boils of stress than on one of the country’s 1,900 islands.

But which one? Having stayed on six and stepped on to eight more, I am a mere beginner; but I love Homer’s Odyssey, so Ithaca beckoned. The island is one of the Ionian chain, where the weather is unreliable at each end of the season but which compensates high-season travellers with luscious greenery unthinkable in the parched Dodecanese, and with a filmy, gauze-like beauty that contrasts with the moonlit purity of the Cyclades or the blanched silences and austerities of Crete. In addition to all the normal pleasures of Greek island life, such as listening to donkeys bray, lapping milky ouzo as you watch tiny boats bob on glittering water, and chatting with some of the gentlest people on earth, I could also trip about in the footsteps of an emboldened Telemachus, hunt down the pig farm of faithful Eumaeus, and locate the vineyard where tired Laertes hauled himself along the steep slopes during his ill-rewarded retirement.

Or so I thought. Then a Greek friend asked me if I’d read Robert Bittlestone’s Odysseus Unbound (Cambridge University Press). This recently published book – which, at just over 2kg, constitutes excess baggage on its own – makes an entertainingly energetic and often convincing case for Homer’s Ithaca in fact being the relatively low-lying, western peninsula of Cephalonia, known today as Paliki. Poseidon the earth shaker has been abnormally active hereabouts – the African continental plate collides with the European one along the Cephalonia transform fault, unleashing a sizeable earthquake every 50 years or so (the last catastrophe was in 1953). The whole place has, thus, been rattled like a tambourine throughout recent geological times. It is Bittlestone’s contention that a channel once separated Paliki from the rest of Cephalonia, which would explain Odysseus telling Alcinous and his court that his Ithaca “lies low and away, the farthest out to sea,/rearing into the western dusk/while the others face the east and breaking day” (Book 9, lines 27-29 in the Robert Fagles translation, published by Penguin). Modern Ithaca, according to Bittlestone, was Homer’s Doulichion, where Penelope’s loathsome suitors came from. This is not the moment, and I am not the scholar, to pronounce on the theory, though I did note that in Book 4 Telemachus tells Menelaus that there is “No running-room for mares in Ithaca, though, no meadows./Goat, not stallion land, yet it means the world to me”. These lines apply more fittingly to mountainous, goat-ridden modern Ithaca than to Paliki, whose topography is relatively gentle and whose farmland continues to flourish. Other aspects of Homeric geography, too, are decidedly squiffy, as Bernard Knox points out in his introduction to Fagles’ translation, so should we expect literal fidelity in the case of Ithaca?

There are named Homeric sites on modern-day Ithaca, but apart from the enjoyable walks they provide, all are scarcely worth bothering with; to call them hopefully vague in attribution is charitable. The museum exhibits, too, are disappointing. Surprising? Hardly; the Odyssey is a narrative poem composed, probably in Asia Minor, around 2,700 years ago. Its importance to mankind is its ability to charge our imaginations with undiminished power. Set besides this great heartbeat, the hinge linking it to precise geographical realities is a mere appendix. I took the Odyssey to Ithaca, and ended by worrying far more about the total contempt in which a good fish supper was held by the book’s obsessive carnivores than I did about being on the wrong island.

Imagination, I began to realise, is the key to a holiday on any unspoiled and undeveloped Greek island. What do you do once you’re there? You could buzz about in a hire car trying out different beaches and tavernas, and hire a boat to explore those otherwise used only by goats taking their annual bath. A certain amount of this is fun, and we did both. Ithaca’s beaches are all pebbly, most of them set in pretty bays; even in August, there were rarely more than a dozen fellow users, and the water is glassy; it is not hard, with a little boat at €50 per day, to find a virgin beach for yourself. To understand the land, perhaps, it is necessary to cross the water.

The walking, though, is still more inspiring. We stayed in the small village of Kioni, unquestionably the island’s prettiest location: its neat little amphitheatre of hills winds down to a turquoise bay fringed by rock-stunted pines and protected by a low, distant arm on which three ruined windmills stand, basking in the evening sun. The two-hour path from the village to the former capital of Anoghi, 500 metres up on Mount Neriton and well out of the reach of the pirates who plagued the Ionian islands in the Middle Ages, is glorious, especially if you embark before dawn: the first rose light spills across a sea so still it could be locked in sheet ice, while all around you the goat bells echo in the valley like a gamelan concert. By the time the sun gilds the water and the ferries cut their way across it, you are standing in a scented stonefield of pale green wild sage; from there, the path rises through a dappled forest of holm oak, passing a large stone well where someone – shepherd or sailor? – has fastened an icon of St Nicolas to a stone post. The final stretch (by now the lizards are scuttling companionably) gave me blackberries to graze on; the feathery sea squills pushing out of the boulder-strewn earth showed that autumn was beckoning.

But, once installed, why go anywhere? The deepest joys of two weeks on an unspoiled Greek island are those that come as you take possession, imaginatively, of a small landscape. Two car-less weeks in Kioni make you part of the place. Simply sitting, as fierce midday approaches, underneath the breeze-ruffled pines next to the church at the top of the hill was exquisite; an old man came to join me every day, where he monitored a tiny transistor radio and drank a small orange juice. There were others: the easy pace of Greek village life, where most of the day is spent gazing or talking, fertilises human contact. And humanity was everywhere: arriving at the village shop with no money one day, we were not only allowed our shopping on credit, but smilingly invited to take the whole shop if we wanted it. Watching the yachts come and go in the harbour was a lesson in the delights of non-ownership: what cumbersome and anxious possessions they are, and how socially traumatic to berth. I looked down at the tiny fishes, rocking with the crystal waves along the harbour shoreline, and understood freedom a little better. Listening to a pair of buzzards mew to each other as they quartered the nearby hill; battling the Ithacan mosquitos, each as wily as Odysseus; watching the rats tumble out of the olive groves as dusk approached; resting at night as cockerels and dogs each try to have the last word on the closing day: all of these moments, whether they slow or quicken the heart, marked the otherness that refreshes. Nowhere combines simplicity with beauty quite like Greece, and Ithaca – or Doulichion – set it against the deepest cultural backdrop of all.