Walk out along the causeway from Naxos Town, which everyone calls Chora, and the Portara grows from a distant frame into a structure of staggering scale, two upright marble blocks and a lintel that have stood since the 6th century BC. The temple behind it was never built, and that incompleteness is the point: the doorway opens onto open water and changing light. Sunset is the moment to be here, when the marble warms to honey and the islet fills with people who have come to watch the sky burn behind the gate. The locals swim on both sides of the causeway, and where the eastern water deepens, on a calm day you can dive down to find ancient columns that toppled from the temple and now rest on the seabed.

Naxos is famous for beaches, and most of the island's west coast is effectively one long ribbon of sand washed by clear azure water. South from Chora they come in a string of names worth learning: Agios Prokopios, Agia Anna, Plaka, Orkos, Mikri Vigla, Kastraki, and Alyko. Some catch the wind just right and have become magnets for windsurfers and kitesurfers; others, screened by dunes and trees, are quiet enough for naturists. The further south you go, the more the crowds thin out. Over on the eastern coast the mood changes entirely, where the tiny harbours of Lionas and Moutsouna stay picturesque and calm even in high summer, each with a taverna and a beach and a newly paved road threading past secluded bays.

Most visitors never leave the coast, which is exactly why the centre of Naxos is so rewarding. Head about 10 kilometres inland and the flat shoreline gives way to lush green mountain valleys, ancient olive and lemon groves, and narrow gorges where streams run past terrapins sunning on the rocks. This is the most fertile of the Cyclades, green where its neighbours are brown, kept watered by mountains high enough that fully cloudless days are rare. The villages here are older than the beach towns, with Bronze Age roots, perched high with steep, twisting lanes built to confound pirates. Halki shows off elegant neo-classical houses beneath a cluster of red roofs; Apiranthos dazzles with marble-paved alleys, arched passages, and four small museums; and Filoti climbs the slopes below the island's great peak.

Above the valley of Filoti rises Mount Zas, also called Mount Zeus, and at just over a thousand metres it is the highest point in all the Cyclades. Its marble slopes climb steeply to a sharp summit, and on a very clear day you can see all the way to the coast of Turkey. The path up from the Agia Marina chapel on the north side is the gentler route, marked and dotted with fresh-water fountains; the southern approach is steeper, rockier, and passes the cave once linked to the infant Zeus. The climb rewards the effort with one of the great views of the Aegean, a slow turning panorama of islands scattered across the sea in every direction.

Naxos sits at the heart of the Aegean ferry network, a few hours from Athens by boat and just two from Santorini, with a small airport offering quick hops from the capital. On the island, a quad bike is the traveller's friend, more stable than a scooter and narrow enough to survive an encounter with a truck on a blind mountain bend, with the bonus of an open view as you drive. Ten bus lines reach every village, though some only three times a day, and the morning bus runs full of local grandmothers heading to market. Try the island's own kitron liqueur, distilled in Halki from an exotic citrus, and the famous Naxian potatoes. Be warned: the island has a way of holding on to people. As locals like to say, plenty of visitors meant to stay a few days and never quite left, living proof of Ariadne, the Cretan princess abandoned here who became, in the old myth, the bride of Dionysus.