Finding a restaurant when staying in Kinira is a task. In fact, if you're looking to go out to a restaurant every night, you might want to stay in another town, or come here only in the main season.
When I was in Kinira, we had dinner booked with our hotel, and although the selection was small, it was fine. If we didn't like the food once in a while, however, we had a problem.
I think there is one tavern and one pizzeria in Kinira, but they both closed when we were there in early May. We either ate at the hotel, drove into the nearest town to eat, or just went up to the local shop to get some cookies and ice-cream. The local shop was tiny and the owners only spoke Greek (Kalimera! Kalispera!), but were very very friendly.
Favorite Dish: Thasos has all the good Greek food one can imagine.
Specialties in Thasos often are made with honey. The island is famous for honey and one special dessert is a fig in honey.
It's really quite quaint. You will be walking along a one track tar/dusty road, and find seafood dangling from a piece of string, drying out... lol
Favorite Dish: The seafood is rather good ;)