Sea food is the base for most of the typical dishes and it follows the traditions of the Portuguese Azorean people who colonized the island.
Shrimp is popular and the standard dish is " Sequência de Camarão" which is the Shrimp prepared in different styles (steamed,fried, etc) and served in sequence.
Fish is also popular, cooked in many ways and usually served with rice and Pirão ( like a paste made of fish).
During winter, the Tainha fish ( Mugil liza), similar to the striped mullet, is the most commom one and it is served stuffed-baked.
In Costa da Lagoa there are many waterfront restaurants serving great seafood and relatively cheap, but to get there you need to get a boat from the Lagoa centre marine. Lagoa Azul restaurant (trapiche 9) is a good choice for value.
In avenida das rendeiras, Lagoa, there are some restaurants very popular with tourists, like Casa do Chico, as they serve the standard dishes.
Santo Antônio de Lisboa and Sambaqui are good places to have a drink and eat Petiscos(small food served in portions), watching the sunset in the Northern bay. Floripa Oysters are famous and the best restaurants can be found at Ribeirão da Ilha Azorean Village.
If you are looking for a more economic option and also want to sample the standard Brazilian food ( rice and beans, pasta, salad, etc), you can eat at restaurants per KILO, where the food is served in buffet style and you pay per weight.
Nowadays, Pizza it is as Brazilian as Feijoada, so Pizza places are everywhere and many have RODIZIOS (eat as much as you want, pay one price).
Making Brazilian friends might give you the chance to be invited to a CHURRASCO, the typical Brazilian BBQ.