If you visit no other beaches while visiting Vieques, make it a point to spend some time soaking up the rays at the aptly named, Sun Bay. You'll also be delighted to see the many wild horses that roam through the park.
There are basic facilities here -- bathrooms and showers -- and decent food is available at a cafeteria near the parking lot.
If you feel like hiking a bit further, you could go beyond Sun Bay to the other well known beaches further East. Media Luna, or "Half Moon Bay" and Navio, the surfer's beach which are further down the coast, are also beautiful spots for a morning or afternoon of sun bathing.