I think this depends greatly on what kind of adventure you are looking for. Having worked as a scuba instructor - I find people are of two generalist buckets. They are either group enthusiasts, or explorers.
Group enthusiasts prefer to find a resort style setup, dive with a crew of people - and have lots of big places that are full of people to dine or drink (in moderation of course, because you're diving ;-p ). For that - I could recommend - Grand Cayman, Northern Belize, Cozumel, Providenciales in Turks & Caicos, Grand Bahama, most of the Virgin Islands, the ABC's - Aruba, Bonaire, Curacao. Some of the resorts in the Dominican Republic can be like this too. I do not recommend Jamaica, and have heard that all but off island diving in Puerto Rico is not worth it. Although I don't have first hand knowledge there so I may be wrong.
For explorers, there are still several places that are unexplored/pristine. Turks & Caicos - Grand Turk, South Caicos & Salt Cay all have spectacular wall diving and will be intimate experiences. All dives are 5 mins from shore, and the wall goes down 7000 feet. Some of the outer islands and southern locations in Belize are good too, although I believe the diving on that wall only gets really good when you go south. Panama, Nicaragua and Honduras have really spectacular locations that are not all that touristed. Harder to get to and more spanish involved, but the fish life is 10x that of Belize. If you go to Honduras - Roatan is better than Utila for these divers, as Utila is crowded with college kids. Roatan is actually unique as it could have the group enthusiast vibe too - all depends on where you stay. And the Bahamas are FILLED with places that are great. Lots of sharks there still, and fish life is generally good. Stay away from any island with a giant hotel and the diving will likely be superb.
Also - some of those live aboards are fabulous ways to go. You really get out to places that are unexplored, and get your own little party that stays with you all week (may be a good thing or a bad thing!).
I'd also weigh the timing you are going as well. January through May the west indies are great because the whales are coming through. Hurricane season... you either want to go far north and pray or really far south. Late fall, its colder so going farther south may mean warmer diving.
Good luck - you really can't go too wrong. Never had a bad dive in my life - all of them are great for their own reasons!