I've been to many of the really good Caribbean locations (Bonaire, Grand Cayman, Curacao, Roatan, Utila, etc.) and find that I prefer liveaboard diving. For one thing, it's basically effortless - just gear up and go 4-5 times per day. No lugging gear around and stumbling over the ironshore or whatever. Also the diving I've done has been more varied - after about the 3rd day, everything on Bonaire started to look similar. Also I like larger stuff like sharks, turtles, rays etc. as well as small stuff.
Unless you want to do Blackbeards, I doubt you'll find a week for around $1000. Sometimes Cat Ppalu - the 3rd Blackbeards boat - sells unfilled charter space for around $1500 - they're also out of Nassau.
Another option is to get on Explorer Ventures mailing list - for their specials they often advertise $500 off per person. Their lower cabins on T/C Explorer are $1895 so at $500 off that's $1395 plus port fees of IIRC $115. Provo is about $6-700 R/T from here depending on time of year. They pick you up at the airport for $40 r/t so that plus dinner in town Friday night and crew tip are your only other expenses. The price includes all meals and their alcohol. Nice thing about the Explorer is it has 3 decks and real cabins, not shared bunks like Blackbeards. Also even the lower cabins are en-suite and there's no water restrictions. It's also twice as long as the Blackbeards boat and much more roomier obviously.
They also offer the same deal on their NE Caribbean trips - Saba/St Kitts. but from here we couldn't make the flights work economically or w/o long travel times or a layover.
We did Turks/Caicos last spring, saw lots of sharks, so many rays it was boring, turtles, barracuda, big lionfish and lots of reef fish. Also lots of tiny fish colonies surround many of the coral heads, I shot some macro one day within sight of the boat. At French Cay and West Caicos the wall is really healthy since it's just off a deep trench so there's lots of nutrient upwellings. We didn't see any but there's supposed to be some big grouper there also. And an occasional dolphin.
Another option from here (Phx) is the Sun Dancer out of Belize. It's $1895, flights are $4-600 and they pick you up at the airport. There's 2 non-stop flights daily. Beats the red-eye to Bonaire...
A last option might be the Midriff Island (Sea of Cortez) trips on Rocio Del Mar. While more $$, ($2295) the boat is almost new and leaves out of Puerto Penasco (Rocky Point) There's a shuttle from Sky Harbor that's $100 r/t. Afaik, the only other expenses would be the $25 park fee and crew tip.
hth,