This article first appears in Vol. 27: Books.

Islands Islands have a boundless appeal. There's something about being cut off from the mainland that stirs the senses and invokes a distinctive state of mind. They signify both limitation and escape, retreat and return. I grew up on a tropical island - Singapore - and have long been enthralled by the faraway, magical islands of Greek myths and legends. My first novel, Ponti, was set entirely in Singapore, and my home island shaped the territory and soul of the story - it was its own narrative force and character. This spring, I'm working on a novel that interweaves aspects of classical and Singaporean mythology. I'm interested in the paradox of placelessness and the overwhelming aura of spaces real and imagined. It's with this in mind that I set out on a journey to retrace the mythology and explore the mood and mentality of the Greek islands of Ithaca and Kefalonia, which have long captivated my imagination.

I arrive in Kefalonia after nightfall. Lit-up homes and small churches dot the mountainous terrain and even with half the landscape obscured, the island has a quiet grandeur. In the port town of Argostoli I am welcomed at the Kefalonia Grand Hotel with a cool lemon drink. Commanding a view of the harbour, this boutique hotel is airy and modern with a sleek, monochrome facade - but I don't have long to explore. In the early morning I rise to catch the half-hour ferry to Ithaca. Approaching its sun-tipped mountain ranges, the stresses and structured rigour of city life give way to pure awe. Time slows down and seeps into the roots of its olive trees, while ancient history is pocketed in its ruins and ocean coves. It's hard to separate Ithaca from Homer's epic poem, The Odyssey, which cemented the island's reputation as the idyllic homeland the hero Odysseus returned to after 20 years at sea. Homer famously describes the "wine- dark sea" and "bright Ithaca", and I'm looking forward to seeing how much the reality matches up to my imaginings.

As the ferry docks into Piso Aetos harbour, the landscape thrums with mythic resonance. Sun glitters off the surrounding waters. Snaking roads encircle evergreen woodland, lush and diverse. The Ionian earthquake of 1953 devastated Ithaca and its surrounding islands, resulting in a landscape of newer Venetian and English-influenced buildings mixed with the shells of ruined, yet strangely beautiful, Renaissance architecture. The island covers roughly 118 square kilometres and its mountains are peppered with ruins, caves, springs and small villages. It is ideal for leisurely hikes, although a car or bike is still necessary to get around.

Since the 16th century Vathy has served as Ithaca's capital and main harbour, a postcard-pretty village of colourful houses clustered around a crystalline bay. For the next two nights I'm staying at the Hotel Familia, a bed and breakfast boutique hotel housed in a renovated 1890s former olive press building of stone and wood. After a delectable breakfast spread of home-cooked Ithacan pastries, marmalades and creamy Greek yogurt, I choose a random uphill path and end up in front of the serene Church of the Theotokos-Gardelaki, its sprawling cemetery flanked by a contemplative view of the mountains. For lunch I find my way to the local favourite MPatis - endorsed enthusiastically by the governor of Ithaca himself, the warm and hearty Mr Spiros Tsintilas - for tangy tzatziki followed by fresh-from-the-net, grilled squid and sea bream with a squeeze of lemon.

Vathy is a convenient base to explore the traditional villages nearby. The quaint and pastel-hued Kioni is a short drive away and is made up of tile-roofed houses overlooking a port of fishing boats and docked yachts. Taverns, trinket shops and restaurants line the waterfront, including the terraced Lizzy's Restaurant-Bar, overlooking an expanse of water of a shade so distinctively, dreamily blue that it has its own name in Greek: "galazios". In the cinematically quaint village of Frikes, I devour zingy berry ice cream at the Dodoni dessert parlour before setting off toward Stavros and Exogi in search of Homer's School. The archaeological ruins are said to be what remains of Odysseus's palace and have an appropriately majestic view of the surrounding terrain.

Hiking up a dirt path, I stumble upon a rusty, old well and crumbled antechamber and think about Penelope, Odysseus's faithful and wily wife, weaving and later unpicking her absent husband's burial shroud to stall her greedy suitors. I consider whether there's a worthwhile analogy to be made between weaving and unpicking, and the meticulous repetition and purposeful deletion that comes with novel writing. I also wonder about all the fabled and unknown people that have lived here, these stately stones their only trace. Before returning to Vathy, I stop off at the Kathara Monastery, which has a breathtaking and poetic aspect of the Ionian Sea, although as dusk begins to fall I find its quiet grounds a little eerie.

The next day I seek out Anogi, one of the oldest and most mountainous villages on the island. It's a rustic and sparsely populated place surrounded by prehistoric natural rock formations. The largest of these, known as Araklis, is nine metres tall and otherworldly to behold - the clearing of prehistoric stones fringed with dried-out trees and shrubs resembles the site of an extra-terrestrial landing. Hiking through sunny Perachori, I make my way to the ruins of the medieval settlement of Paleochora, whose denizens were once so afraid of pirates they built their houses without windows. Its three churches house Byzantine murals and are havens of meditative calm. Toward sunset I follow a winding path down to Ioannis Beach. I have the entire white-pebbled stretch to myself, so I compose a smug Instagram post and then lie on a towel reading as I enjoy the lapping of the waves. I try to write down some fragments for my novel, but all I can come up with are paltry descriptions of paradise. Ugliness and grit, I feel, are easier to depict than overwhelming beauty.

The next morning I take the ferry to Sami on the island of Kefalonia, where I make a beeline for Myrtos Beach, frequently listed as one of the best beaches in the world - and for good reason. Dramatically framed by steep cliffs, it's a curved stretch of meringue- white sand and cerulean sea blended into foam green by the surf. It's so pretty I get optical overload, as if my jaded city eyes can scarcely believe so much beauty. I have a beer on the beach before setting off for Assos, a small town built amphitheatrically around a peninsula. Feline lovers take note: I have never seen a larger quantity of adorable cats basking than on these sunlit streets. I leave the cat gang and stroll along the Fanari trail, going past ascending layers of sloped gardens blooming to burst with vivid flowers and monstrous succulents. The passage opens out to a panorama of the surrounding islands rising out of the sea like giant green humpbacks.

Towering over the village is Assos Castle, a Venetian fortress accessible by a pleasantly winding stone path. The ruins and castle grounds at the top of the rocky hill are plucked straight from a fairy tale, all cobbled pathways and enchanting herbs and flowers. I end the day with a visit to the impressively regal Saint Gerasimos Monastery, decorated with shining frescos and murals depicting scenes from the Old Testament and the Last Supper. Gerasimos is the patron saint of Kefalonia, famous for his healing powers. According to local legend, there were numerous visions and sightings of him around the island after the 1953 earthquakes.

Driving to the other side of Kefalonia, I check into F Zeen, a family-run boutique hotel built into the hillside next to Lourdas beach, with space-age, yoga-chic vibes - I half expect Tilda Swinton to appear in a grey tunic telling me I have completed my mission and can finally rest here. I peer out of my bay window over the Ionian Sea, a broad shimmer smudged in pinks and oranges as the sun sets. There's no questioning that the Ionian horizon is deeply romantic, and when I make my way to the restaurant I find myself surrounded by young, canoodling couples. "Oh, fresh love!" I think, the serenity of the space making me more benevolent than usual. I would probably roll my eyes if we were all on a tube carriage.

After a breakfast feast of locally sourced honey, figs and fresh fruit with strapatsada (scrambled eggs with cherry tomatoes and feta), I visit Melissani Lake, a lacustrine cave and subterranean pool. I feel like a poor soul being rowed into the underworld as a singing ferryman guides my boat through waters in changing shades of lucent blue and teal, past a narrow opening that leads into a dark cave and a small island with its own vegetation. The stalagmites and mineral formations give off an ominous atmosphere, exacerbated by the ferryman telling me there are eels in the water and huge bats in the air. Fortunately, I see none of either before the boat makes its way back into the exposed chamber and the sun hits the rock wall right on cue, setting off a jewelled chiaroscuro on the lake's surface.

I drop into the nearby Drogarati Cave, which was discovered 300 years ago and opened to the public in 1963. Huge stalactites and stalagmites are suspended from a high ceiling in what is known as the Chamber of Exaltation, which is the size of a vast banquet hall and contains a sense of mystery and adventure. I later learn that the cave is around 150 million years old and has an unreachable extension that goes even further into the earth.

On my final morning in Kefalonia, an almighty rainstorm renders the once bright-blue sea as grey as steel. I think of the gods Zeus and Poseidon waving their staff and trident around for the fun of it. I go through the notes and sketches I've made about each island and what marks them as particular. Despite being so close together, they both have their own distinct character: Ithaca feels palpably steeped in history, mythology and a kind of timeless, unvarnished magic, while Kefalonia is all exquisite natural beauty and storybook-like whimsy. The experience has proven to be majestic, transportive and grand. As my plane ascends steadily above the islands and the sea, I pick up my pen and begin to write.