Wow!! Congratulations, that is so great you won tickets. You didn't really state what your budget concerns are, but since everyone likes to save money and have a great time, I have to whole heartidly recommend the Dominican Republic.
Out of the places you listed, I have been to 3 (I think, can't remeber the list now
I've been to other places in the Caribbean, but they weren't on the list) the Bahamas, Jamaica, and the DR. For what its worth, here's my opinion on each - Bahamas, stayed at Atlantis, and have to warn you, my opinion maybe tainted because we were there with some of hubby's clients, so it really wasn't a relaxing vacation
. It's nice, but not somewhere I am dying to return to. Jamaica same thing, actually the country is very beautiful, but its not really that safe to leave your resort, so that is a big negative to me, plus the resorts are way too overpriced.
For the best vacation value you really can't beat the DR. Normally hubby and I go to the Mayan Riviera on Mexico's Caribbean side (cause it's the closest for us), but this past Sept, we wanted to try something different, so I picked the DR because I had heard so many great things about it. We both loved the DR, mostly because honestly, the Dominicans are some of the most friendly people we have ever encountered. The country is really lush and beautiful. The resorts are incredible, and really reasonably priced, the cheapest you will find in the Caribbean. We stayed 4 nights in Santo Domingo, just because I really wanted to get a feel for the country, and not just stay at a resort, and then we went to the RIU Palace in Punta Cana for a week. This is a beautiful resort.
The funniest thing, as we were leaving and flying over, I told hubby, this is a country I would love to return to, but didn't really think I would, because it is very far for us to fly (takes about 13 hours (with connections, etc.)for us from the West Coast!!), and I like to try different places. Well, turns out, hubby just qualified for an incentive trip at work that we didn't even know about that happens to be for Valentine's week at the Caso de Campo in the DR. This is suposed to be the nicest resort in the DR, so I'm super excited!! But quite honestly, I would be happy with any trip to the DR. It is really a very beautiful country.
I am sure you will love no matter where you decide to go - any trip to the Caribbean beats the heck out of work!!