Atlantis - Paradise Island - Bahamas
Or be a cheap skate and stay next door at the comfort inn, but have free access to all the atlantis facilities
I have visited about 16 Caribbean islands as part of a cruise back in 2001. Plus I've been to the Bahamas about 5 times.
As mentioned above, Atlantis, this will be the most upscale part of the Caribbean. (Really its for tourist Americans wanting a Disney like experience) The Bahamas is an otherwise small island...
Other places that are nice, are any of the European governed islands, such as St Maarten, Martinique, St Thomas, Aruba.. The self governed islands, outside of the main downtown, which will include some colourful architecture, will be quite shanty and mostly rundown.. Obviously the beaches are nice ALL OVER the Caribbean, and the inland is typically tropical forest like. Some have nice trails, with waterfalls etc...
Have you thought about a Cruise, and visiting a few of them?
Also end of May, that's getting close to Hurricane Season, which starts on the 1st June... You'll be subjected to heavy rains every afternoon like clockwork, if your holiday extends into June. It's also getting too hot around that time. Now is the PERFECT time of yr to go, if you're able too.