Tortola has good diving but it's pretty close to St. Thomas so is similar. Nice reefs, lots of fans/soft corals, the occasional shark. Depends on where the dive operator takes you - some of the islands (Norman, Peter Cooper, Salt Islands etc.) just south of Roadtown are pretty great. We also did good dives amongst the Dog Islands slightly NE. IDK if anyone is doing the Rhone wreck (off Salt Island) on a cruise day trip but it's excellent.
Admiralty or Blue Island Divers will likely take you south off St. Thomas - possibly to a wreck since there's a lot of them nearby. Both pickup at the Havensight cruise port.
On Nassau, Stuart Cove's shuttles you from the cruise port to their south side location. About 1/2 hr+ each way. If you're in early enough, Bahama Divers is another option. With customs clearance you probably won't be - their 2-tank leaves at 9AM.