I was really impressed with the Nisbet Plantation on Nevis. Very quiet, private, and luxurious in an understated and classy way. Their beach was mediocre, though. It may be closer to $700 a night IIRC, but check and see if they have any specials.
Nevis is cool, but not super-scenic like Tortola, or someplace. Some really nice plantation stuff, some great restaurants, but I was not very impressed with the beaches in general. But if I were just going to relax at my resort and maybe go out in the evening for dinner, the Nisbet would be near the top of my list.
I think I had to fly through SJU, but maybe you could get there through MIA.
I think St. John is one of the most beautiful Caribbean islands I've been to, with splendid beaches, but I have only day-tripped there, and don't know the hotel situation. It seems to be pretty high-end, though. Easy to get to.
I have spent some time time working or vacationing on, let's see, Puerto Rico (incl. Vieques and Culebra), St. Thomas, St. John, Tortola, Jost Van Dyke, St. Martin, Saba, St. Kitts, Nevis, and Dominica. I can try to provide helpful opinions on any of these places if one of them interests you. I'm more of a go out and explore rather than a hang around the resort/beach type of guy, though, so YMMV.