Sharks are a given with Stuart Cove's on Nassau because they feed them. They also hang around nearby sites waiting for the feed.
Sharks/Dolphins with UNEXSO on Grand Bahama are also likely - Sharks are fed and there's a Dolphin program.
Eagle Rays, Stingrays, Tarpon, Turtles are common off Grand Cayman. Not many sharks though. Stingray City is a given.
Non-fed Sharks, Stingrays, Barracuda, Turtles, big Grouper, sometimes Dolphins in the Turks/Caicos. More likely off West Caicos or French Cay - about 45mins. by boat from Provo(Providenciales). There's both an Aggressor and an Explorer liveaboard that go out there weekly also.
We saw a few Sharks, Large grouper, Oceanic Triggers and snorkeled with Whale Sharks off Utila - Whale Sharks are usually only in the spring.