I spent a week in Grand Cayman with the fam around New Years. Awesome trip. Not a lot of culture, but 7-mile beach is pristine, the Caribbean was warm, locals were friendly, and it was very clean and safe. Very expensive though. Pricey to begin with, but then you are also only getting like $.80 to the dollar so it's compounded. Relatively easy to get to from ALB (Delta with a connection in ATL).
I don't know anything about The Bahamas except what i have read about the newish Hyatt, and seen from the Fyre Festival documentary. I thought i recently saw that there is a travel advisory there now.
I've never done an all inclusive because my wife and I dont really drink (enough to make it worth while). I think Jamaica and the DR are the two hot beds for those accommodations. This lady who blogs on personal finance and travel swears by this place.
Holiday Inn- Montego Bay
There are a few threads where people listed their favorite vacations. Lot's of Caribbean mentions.