I've traveled across the Caribbean. A lot of the islands are six and half a dozen of each other. Here's my thoughts.
My favourite destinations:
Aruba: Yes, it's arid, but there's a lot to do there. Some of the most beautiful beaches and great restaurants, shopping. The nearby reef and sunken ships add plenty of opportunity for snorkeling and scuba diving.
Cuba: Sadly, you guys can't go yet. Which is good for us because it's only loud French Canadians we have to deal with. The people there are super nice, and it's one of the safest islands to travel. Old Havana is a must-visit if you like history.
St Martin: Beautiful island with good shopping and decent beaches. Not much to say about this one.
Grenada: The spice island. If you're looking for tropical, this is it. Also a great culinary experience.
Barbados: Not much to say about this one either. It's the richest island in the Caribbean, but still offers tropical atmosphere if that's your thing.
Least favourite
Antigua: The home to AnyDVD and not much else. People here were very rude.
St Lucia: It's a rundown and impoverished island, that never feels quite safe. Outside the luxury resorts, there's not much to do here.
US Virgin Islands: Nothing particularly wrong with these islands except that they're heavily Americanized. It felt like a trip to Florida.
Neutral
Puerto Rico: Old San Juan is cool to visit but can be done in a day.
St Kitts and Nevis: A quiet spot to visit if you're looking to just veg out for the week. Nothing else beyond that.
Curicao: Like Aruba but not quite as nice as Aruba. Go to Aruba
Bahamas (Nassau): I made the mistake of going during Spring Break. A drunk frat boy tried to steal my hat. I guess that soured my impression of this island. Outside of that, the whole island feels like a giant tourist trap. Go there for Atlantis and nothing else.
Not sure what to pick? I highly recommend a cruise. Lets you see multiple islands, because most of the attractions there can be seen in a day anyway. Stay away from Carnival and Royal Caribbean and look for smaller, more intimate ships. You'll have a better time.