You will find amazing restaurants both casual and more formal. My recommendations include:
Mordisco: Located on the food oriented Paseo de la Concepcion at number 10 in Eixample, it is lovely restaurant and a good place for a casual meal if you want to eat before 9 pm.
Grupo Tragaluz owns a number of restaurants in Barcelona, Girona and Madrid, including Tragaluz: I enjoyed Tragaluz which was the original restaurant in the chain. It is at Paseo de la Concepcion #5. There is a Japanese sushi bar and restaurant on the first level and a restaurant upstairs featuring Mediterranean cuisine. It is an attractive restaurant with good food. Upstairs was a more business-oriented crowd while downstairs was much younger.
Cerveceria Catalana, Calle Mallora 236: I liked this large, attractive restaurant serving tapas with both indoor and outdoor seating. I had a really well cooked cuttlefish and other seafood just off Rambla de Cataluyna.
Dos Pallilos, Carrer Elisabets 9: What do you get when you combine a chef, Albert Rauwich who worked at El Bulli for 10 years, and Asian cooking? You get a truly amazing meal at Dos Pallilos. Located next to Casa Camper, a sleek contemporary hotel, the restaurant is a short walk from Las Ramblas. It has more of a tapas bar in front and a larger bar in the back where diners sit watching the food preparation. It offers two tasting menus. I opted for the larger one with around 18 small plates. The food was really outstanding!!! I highly recommend it if you like the food of Japan, Thailand, China and Vietnam. The staff was great and helped make it a very special evening. Head chef Takeshi Somekawa is also an El Bulli trained chef.
La Boqueria on La Rambla 91: This is one of the best food markets in Europe according to many sources. It has wonderful produce, meats, fish, cheese, chocolates and sweets. I had lunch at El Quim de la Boqueria which was highly recommended. It was a really great choice. I would suggest going early, around 12:30, to get a seat at the bar!
Other restaurants to try include Disfrutar which is known for its creative, gourmet tasting menus and Barraca. Barraca is located on the beach in Barceloneta and it is known for its paella and fish dishes.