There are many taverns and restaurants on Santorini. The most are not bad, but they have been adapted to mass tourism. There are still a few that have preserved their traditions and warmth towards the guests. One of these recommendations is the beautiful tavern near the Minoan excavations of Acrotiri, the "cave of Nikolas". You find it easily if you walk directly from the excavations down to the sea shore and turn right. It is the third tavern there. The family Alefragkis care with Greek hospitality about all guest and Mrs Margarita Alefragkis is one of the best cooks on Santorini. Her son Minas is organising the fresh fish and other food and helps out even as a waiter some times. Margarita has won culinary contests about Greek food and her tomatokeftedes are the best of the island! Everything is fresh cooked and the setting directly at the sea shore is great! The prices are still affordable.
Also you can enjoy Margarita´s brother´s tavern Kyma next to her and get great sea food there. If Jiorgos is in good mood you may even enjoy live music.
The other tavernas on the beach are not bad, but the "Spilia tou Nikolas" is the best!