Nassau: Stuart Cove’s without a doubt.. Great dive spots, including movie sets, professional service, (although can be cattle boat style at times) and sharks, sharks and more sharks.
Half Moon Cay is Carnival’s Private Island, so if they do anything like Royal Caribbean, they will have a guided dive excursion offered by the cruise line for that stop. (Only cruised Royal, so I don’t know how/if Carnival does it)
Pensacola has MBT Divers, among others.. I used them when we did the Oriskany and enjoyed them also.
Hope this helps..