There are no signs to the hot spring, but I locate it on the map and we drive to the end of the paved road. Overlooking the sea is a stone bench someone has dedicated to her parents, “with gratitude and love as deep as the Aegean”. My dad died recently and the words strike home. I’m glad my mum has joined me on this little adventure.

We walk down to the deserted cove at Agia Kyriaki thermal springs. There are old fishing shacks with stone-slab roofs, and shuttered cottages. Down an unmarked path, we find a rock pool where hot waters bubble gently from the sand, blending with the sea to a perfect temperature. Immersed in the healing mineral bath, I look up at juniper trees and blue sky, lulled by lapping waves and cicadas.

Ikaria, in the eastern Aegean – named after Icarus, the Greek mythological figure who flew too close to the sun – is known for its forests, springs and wine, communist leanings and longevity. Its population of about 8,000 is spread across dozens of scattered villages over 255 sq km, with few dedicated to tourism, and it only really gets busy in July and August. We arrive in mid-June from Kos (ferries also connect Samos and Athens to the port of Evdilos) at the port of Agios Kirykos and drive north-east to Faros, which has a mile of beach without a single hotel. The house we’ve rented for our first few days, Lighthouse Lodge, is perfectly located next to a cafe-bar and two tavernas – the hot spring a few kilometres away.

While Mum reads in the shade of a tamarisk tree on the beach in front of the house, I walk around the mastic- and thyme-covered cape to Drakano tower, with remains of fortifications from the fourth century BC. The lofty peak of Samos and the Fourni islands are the only features in an expanse of blue – the space and light are mesmerising.

A few Greek families with young children linger on Faros beach until dark. At Grigoris taverna, we eat grilled sardines and soufiko, summer vegetables cooked slowly in olive oil, and drink Ikarian red wine. Then we fall asleep to the sound of the waves.

The next day we explore the north of the cape, swimming in the clear turquoise waters of Iero bay, near the cave where legend has it that Dionysus was born.

Getting to Monokampi, a pretty village 15km inland from Agios Kirykos, and our base for the following two nights, requires negotiating the forest-covered Atheras mountain, which stretches in a 40km ridge across the full length of the island, rising to more than 1,000 metres. Our route zigzags up a vertiginous slope, cypresses poking up from the tangle of trees.

We’re late and I call George, owner of Moraitika Farmhouse, to say we’re on the mountain somewhere. “Ten kilometres in Ikaria are not like 10km anywhere else!” he laughs. When we arrive, George shows us around what was his great-grandmother’s farm, lovingly restored over 15 years. Three houses are now tourist accommodation, while the oldest one, from the 14th century, is like a museum to old Ikarian life, with a large fireplace for smoking meat, an inbuilt oven and a secret back door for escaping from pirate raids. A forest of arbutus (strawberry tree), oak, olive and ivy has grown over the once-cultivated terraces and the footpath his grandmother used to walk over the mountain.

In the evening on the terrace, as the sun descends over the sea, we eat local cheese with an organic dry white wine, Begleri – all picked up en route, as we’re a long drive from a taverna. Eleonora’s falcons swoop, an owl hoots and there are tiny, bright lights of glow-worms.

In the cool morning, birds sing their hearts out. We walk through Monokampi’s village square, dominated by a huge plane tree, and follow a sign to Agia Sofia, a hidden chapel built into a rocky spur. Mum points out honeysuckle and walnut trees, and we pick mulberries and plums.

The next day we descend to the coast and continue west, stopping at Karavostamo for a swim and fresh spinach pies from the bakery, then we drive on, looking for a place to stay for the next few nights. We stop above an impressive beach at Gialiskari, but there’s the thump of music from a bar so we keep going.

At Nas, we pull in at a taverna. After a lunch of courgette fritters, herby meatballs and homemade cheesecake with sea views, we think we might have found our place. We walk on until we spy a lush river canyon and a sparkling cove, and soon find rooms at Artemis Studio.

Steps lead down the rock to the bamboo-fringed estuary, where swallows and damselflies flit. The other bank is dominated by the walls of an ancient harbour and a ruined sanctuary for the worship of Artemis, protector of nature and wildlife. The waters flow from the deep, pine-covered Halari gorge, which extends several kilometres inland, with paths leading in various directions. The riverbed, with pink-flowering oleander and little waterfalls, fills with wild campers in mid-summer. For now, quiet reigns.

We quickly fall in love with Nas. Mum swims in the freshwater lagoon with the frogs; I swim in the sea, which is cold enough to leave my skin tingling. When the sun sets into the ocean, we settle on Artemis’s peaceful terrace for baked aubergine with kathoura cheese and red peppers, and goat roasted in olive oil and wine. The taverna is run by Thanasis, a musician who offers tours of his family’s organic farm, and Anna, who has a ceramics studio and shop, where we take our time choosing pretty jewellery.

After a breakfast of fresh juice, eggs and Ikarian smoked ham at nearby Reiki cafe, we head on to our next stop, in the village of Agios Polykarpos. We’re staying at Monopati Eco Stay, which has studios of stone, wood and bamboo, with large windows framing a magnificent view of blue sky, canyon and forest.

The owner says we will find his 87-year-old mother in the garden. Svelte and sprightly Popi, covered up against the sun, is thinning out her basil plants and beams at us. She shows us terraces filled with courgettes, sweet potatoes, aubergines and tomatoes. The next day she picks me apricots, shows me how to make basil pesto with walnuts and sunflower seeds, and tries teaching me to dance the ikariotiko, with a deep laugh when I mix up the steps.

Her philosophy is: good food, good thoughts and outdoor exercise. Every morning, she looks at the magic of nature and feels gratitude. “We only have one life – we must make the most of it.”

Mum and I feel that exact sentiment as we wave goodbye. We’ve made the most of our two weeks of discovery in Ikaria. We leave not only revived by good food and rest, but energised and inspired by the sweeping landscapes and time together, with precious memories to last a lifetime.

Lighthouse Lodge, Faros, from £105 a night (sleeps 4, minimum three nights); Moraitika Farmhouse, Monokampi, from £55 per house (sleeps 2-4); Artemis Studio, Nas, from £40 per studio (sleeps 2); Monopati Eco Stay, Agios Polykarpos, from £80 per studio (sleeps 4-6, minimum three nights)