I'd recommend checking out St. Kitts and Nevis. My mother and I used to go to St. Kitts every year for about 20 years; granted it's been about 5 years since we've last been back (due to real life complications and the loss of a few close friends we had on the island) but we really loved it and especially the people there. St. Kitts has a number of really lovely, quiet beaches all along its lengthy peninsula, good for swimming and snorkeling. The main town Basseterre is beautiful, lots of historic British architecture. It's really a fascinating place as SK & N are an independent nation, released from British rule in the early 80s -- and they are extremely proud of that fact! There's a great music festival in June that draws a lot of people but otherwise it is very quiet. We usually stay at the Marriott; even though it's a big resort, it's still got a lot of island charm. Otherwise I recommend the Ocean Terrace Inn on the cliffside of Basseterre. We also used to sometimes rent a condo at the Horizons in Frigate Bay which had some great units a short walk to the beach, but the management was always a little flaky. I'm not sure how it is today.
(Shameless promotion time: I've written a number of pieces about St. Kitts and you can find them all linked/brought together here:
http://sockii.squidoo.com/visiting-st-kitts-a-guide-for-touristsSt. Kitts' sister island Nevis is also well worth considering. It's smaller but has the most incredible Caribbean beach, Pinney's Beach, one of the most beautiful I've ever seen. It's so long that you can find several beach bars along it but also plenty of stretches that are very quiet with no people around. There is a swanky Four Seasons resort right on Pinneys but also several lovely hotels up in the volcano hills on former plantation grounds. I've stayed at Nisbet in the past and we loved it there. (Montpelier Plantation is where all the rich & famous stay.)
I think you can also get Montserrat volcano tours out of St. Kitts, either by ferry or helicopter? If you're interested in that sort of adventure. There actually are operating hotels on Montserrat now, on the side of the island that was not touched by the eruptions and is considered "safe" today. I would love to go back at some point myself (I went twice before first the hurricane and then the volcano activity really hurt the island community.)