On Cayman the Carnival cruise operator is Don
Foster's. They generally use large boats and dive pretty benign sites. There's also 3-4 other options in Georgetown near the port, Deep Blue, Wall to Wall or Lobster Pot at
Lobster Pot Dive Center - a short walk north of the cruise port,
Off the Wall in the same area or
Diver's Down which you'll get to first walking north - IDK anything about them.
Two "signature" dives on Cayman are the
Kittiwake wreck or Stingray City - a 60' tall wreck in 70' of water. As a new diver you'll be limited to exploring the upper decks where they've cut huge holes in the hull so you pretty much always see the way out. And there will a DM in the water with people of your experience level - it's the rules there.
SRC is a dive/feeding opportunity with the Rays - in 15' of water for 45mins. Lots of fun. I'm reliably sure no one has ever gotten hurt there except when the rays "persuade" you to drop the squid. Deep Blue is one out of Lobster Pot Dive who should be diving it in 2018 -
Deep Blue Divers – Take a trip to Stingray City in Grand Cayman There may also be a descendant of "Psycho" the Moray Eel in a coral patch nearby. Harmless but 1/2 blind so don't get too close. If your ship sells Sandbar trips - that's a snorkel only nearby. Sometimes both get called Stingray City.
Dish may not be aware of this but Eden Rock was damaged earlier this fall - a container ship scraped 150' of reef clean. And collapsed one of the caverns. It's not something they can fix so IDK how the diving is there now - it wasn't great to begin with after decades of cruise traffic (500' from the cruise tender dock.
Also there's a plan to build a cruise pier on Cayman - approved but I"m not sure of the construction progress by 2018. One plan I've seen shows Eden Rock covered over by it - also the dredging in going to silt over (and kill) the coral. Georgetown may look a lot different by 2/18. Both are pretty benign dives generally around 40' or less. The big silver fish in the Grotto are Tarpon and have virtually no interest in you. They'll likely let you get fairly close though.
I
wish I'd seen a shark on Cayman's west side. And we dove there every day for a week. It's a pretty cool thing when you do see one and none of them consider you as prey - you're bigger than most and make weird bubble noise. Lately a few may check you out hoping you're a lionfish culler and have a snack for them but that's mostly on the far east north wall or east side - neither location that you'll get to off a cruise ship.
Lastly if you're in port all day, the afternoon boats tend to do shallower dives. Around 1pm so if you're sailing around 4-5pm. it's an option. One thing to ask any operator doing a deeper 1st morning dive is what you'll see if you stay shallower instead. Some sites can be just as good at 40-60' (depends on the mooring/wall location) at others you'll be swimming in blue water watching the other divers 30' below you - not nearly as much fun...