Naxos eats better than any other Cycladic island, and the reason is simple: it produces its own food. The Naxian potato is genuinely famous throughout Greece — chefs in Athens pay premium prices for them. Local cheeses include graviera (sharp and nutty, aged in caves) and the softer arseniko and kefalotyri. The island raises its own cattle and pigs, cures its own sausages, and distils a citron liqueur found nowhere else in the world. Eating well here requires almost no effort.
In Hora, the waterfront is lined with tourist tavernas that are fine but unremarkable — the usual salads, grilled fish, and moussaka priced for visitors who won't be back. Walk two blocks inland and the mood changes. The backstreets of the old town have smaller, quieter restaurants where the food is more carefully cooked and the wine list includes local labels you won't find elsewhere. Portions are generous by Greek standards. For lunch, the covered market behind the main street has bakeries and small cafés serving pies, cheese pastries, and coffee to locals.
Seafood is excellent but order carefully: the words "fresh fish" on a menu mean it was caught locally that day, while "fish" alone often means frozen. Ask the waiter directly. Octopus, sea bream, and red mullet are reliable choices. Island-raised meat dishes — lamb chops, braised pork with local herbs — are often better value than the fish.