A new discovery for us this trip was Sunshine Shack on Rendezvous Bay. It really is just a shack on the beach, but a good place to hang out. The menu is incredibly simple, but the food is delicious. Grilled by Garvey, right before our eyes. There are beach chairs to use and depending on the weather, they offer some fun water activities as well. (Unfortunately, the day we were there it was extremely windy, so no banana boat rides for us.)
Look for it between Anguilla Great House and Cuisinart on Rendezvous Bay. If you want to do some beach bar hopping, walk down the beach to Dune Preserve for another drink or snack.
Sunshine Shack is closed on Mondays, open 10:30 - 6:00 Tuesday - Sunday.