Vieques is small — about 20 miles long, 5 miles wide — and the only practical ways to get around are by hired car, scooter, or públicos (the shared minibuses that run between Isabel Segunda and Esperanza for a few dollars per ride). For the refuge beaches, a car or scooter is essentially required; públicos do not run inside the refuge.
If you stay in Esperanza, you can walk to most of its restaurants and to Sun Bay. Bicycle rental is widely available and the coastal road is mostly flat — a perfectly pleasant way to explore the inhabited part of the island.