Banana’s Beach Bar and Grill (Calle Flamboyan, Esperanza, 787/741-8700, daily 11 a.m.–about 10 p.m., bar stays open later, $5–16.50) is a very casual, popular drinking hole serving mostly American pub fare, including burgers, wings, and hotdogs, as well as jerk chicken, ribs, and grilled fish. There are eight small guest rooms in the back.
Although its prices are fairly low by Vieques [1] standards, the gorgeous ambience of 
Cafe Media Luna (351 Antonio G. Mellado/Carr. 200, Isabel Segunda, 787/741-2594, Wed.–Sun. 7–10 p.m., $12–19) makes it feel like a special-occasion restaurant. Dark blue walls, terra-cotta tile floors, and Indian batik wall hangings set a sensual stage for its interesting combination of Asian and Mediterranean dishes, all made from scratch. Specialties include ginger shrimp pancakes with lemon-coconut sauce, avocado lime cucumber gazpacho, and parmigiana-rosemary–crusted rack of lamb.
Links:
[1] http://www.moon.com/destinations/puerto-rico/vieques-and-culebra/vieques