A major part of Vieques' history involves the U.S. Navy. Many of its beaches, including Red Beach, were named when the Navy operated the island. We were actually trying to go to Blue Beach (the one we'd heard the most amazing things about); however, the roads were too terrible due to heavy rains, and taxis wouldn't bring us. Instead, they offered to take us to Red Beach, a $15 cab ride RT (yes, you need cash here) from where we were staying in Esparanza.
There are 41 beaches in Vieques, and I doubt any of them will disappoint. The island is so small, it basically welcomes beach-hopping. We went to another beach in the morning, ate lunch in Esparanza (so we didn't have to pack food) and then grabbed a taxi going toward the eastern part of the island. Red Beach is too small for a decent walk, but perfect to bring good books and watch the passing cloud porn.
I kind of expected a more remote beach, but this had cabanas and a larger parking lot. Apparently, school had started the week we visited (first week in August), so regardless of what we expected, it was still pretty remote.
I often get the feeling of being "in the middle of nowhere" when I'm somewhere remote on the United States map; and I can say I definitely got that same strange feeling on this tiny U.S. island in the Caribbean.