Check out VRBO when looking - you may find some good deals. That is how we found the place we stayed at last month.

Capella resort would be a great place to stay. There's a beach you can get to right nearby and a further beach they can take you to as well.

In your narrowing things down, did you consider Puerto Rico at all? We spent the last two nights of our last trip there at the El Conquistador resort. we loved it even though we only had 1 day to enjoy it. We tried to do as much as we could though. There seems to be plenty to do there though - they have their own private island with a restaurant. Plus plenty of options at the resort itself. Plus side is that it is very easy to get there as well.