There are a number of nearby islands that can easily be visited in a day. You can go on your own or join a group tour; either option is very reasonably priced. Most people take a boat or ferry, however it is possible to fly. Here are some recommended day trips that can easily be accomplished:
Saba
Saba is a hopefully extinct volcano of just 5 square miles that climbs out of the water to a height of 3,000 feet. There are no beaches. But it does have charming small villages with names like Hells Gate and Bottom. The scenery is breathtaking. The road around the island was only finished in the 1950’s. Before that all goods were carried up villages on donkeys or the backs of men. If you would like to see the undeveloped Caribbean than Saba is a good bet. There are several boats that make day trips.