Tsilivi has a good selection of tavernas alongside the resort restaurants catering to package holidaymakers. The difference in quality and price is significant: the traditional Greek tavernas — those with handwritten menus and a few tables under a vine — serve far better food for less money than the English-menu tourist operations near the beach.
Grilled fish, Greek salad, moussaka, and souvlaki are the staples. Order the grilled octopus if you see it — Zakynthian seafood is excellent. Local wines from the island are worth trying; Robola white wine from Kefalonia (the neighbouring island) is widely available and pairs well with fish. Avoid the meal deals and set menus aimed at package tourists; ordering à la carte from the taverna board produces much better food.