I join with everyone else in recommending Anguilla. It has really come back since the hurricane, of course the beaches have always been wonderful, but they are now better than ever, with Irma depositing large amounts of sand on Shoal Bay east.
You can take the public ferry, $25.00 per person - runs every 45 minutes, a private shuttle from the airport $65.00 pp around 30 minutes, or, you can fly on Anguilla Air Service $100 pp one way, 8 minutes up and down. Be sure to take your passport.
I recommend the public ferry, when you dock, there will be taxi's, tell them you want to go to Shoal Bay EAST, to Elodias. Elodias has chairs, umbrellas, 10.00 per set, plus showers, beach towels, snorkel equipment etc. They also have a good little restaurant with good prices and service, but you are not obliged to eat there. You can rent your chairs and walk down the beach to other places if you are so inclined. Tell the driver what time you want to be picked up for the return, I suggest 3:30pm. On the way back, if it looks as if you have enough time, tell him you would like to see Rendezvous Bay and Meads Bay just a drive by to get the feel of the beaches and the island.
Saturdays are a busy day on the ferry as the locals go back and for to do shopping. Carnival starts August 2, and boats will be busy then too, but Shoal Bay East will not be over run with people.
Happy planning.