To fully appreciate this interesting and beautiful island, you really need to spend a day exploring by car or bike.
As you may know, since 1941, approximately 70% of Vieques belongs to the United States Navy, who run two naval bases, Camp Garcia and Navy Base, situated at the eastern and western ends of the island. Many tourists have stayed away from this island due to Naval bombing practice and an occasional death to civilians. Vieques has been in the news of late with protestors demanding that the Navy leave this island. The US presence has decreased substantially over the last several years but there is still an obvious military presence with planes and helicopters a common site in the skies above Vieques.
You can enter the military areas, such as the beaches at Camp Garcia, which are even more beautiful and peaceful than Sun Bay. Once on the base, follow the unpaved road for a considerable distance until you reach the barracks...continue further and you will see a sign for Red, Blue and Garcia beaches. I found RED BEACH to be the best beach on Vieques if you are a good swimmer since the surf is quite strong. This is also an excellent place to scuba dive.
There are many enchanting beaches, often inhabited by wild horses, a fort built by Spain in the 1840's, and many quaint villages/communities.