If you're fans of Japanese food, you should definitely try Kibuka (Carrer Goya 9, two streets below Travessera de Gracia). Their special makis (9-12€) are out of this world: Hot Philadelphia Roll, Italian Uramaki, Ebi Tempura Uramaki, and Kibuka Uramaki. Their Yakisoba is also great (9,55€). Dinner will run you about 20-25€ per person.
If Japanese food isn't your thing, we recommend La Llesca, a traditional Catalan restaurant (Carrer Teroll 6). For two, we recommend for an appetizer the "llesca con escalivada y anchoas" (bread slice with grilled vegetables and anchovies, 7.20€) followed by the house specialty, "pincho moruno de cordero" (lamb kebab, 7.20€) and "butifarra catalana con secas" (Catalan sausage with white beans, 7€). 15-20€ per person.
For dessert it's typical to go to La Gelatería (Plaça de la Revolució), which is very popular up until winter. The black chocolate ice cream is amazing (2.40€ for a small cup).
For drinks, the bars in Plaça del Sol or Plaça de la Villa with outdoor seating are very nice in summer. Mixed drinks will run you about 7€.