Port Information-
Jamaica: You should book some kind of excursion for this port. It's kind of a dirty port with not much to do in the immediate area. We did the Dunn Falls excursion, which required a very long bus ride to Ocho Rios. It was worth it, but it was very long. I would just say to book an excursion-any!-so that you can actually see something in Jamaica.
The Cayman Islands: Our favorite port! Very cool. You do have to take a ferry to the dock and back (budget 20 minutes for that each way). We did not book an excursion through Carnival, but we were able to sign up for an excursion when we got there for a very good price. We went to the stingray bar and snorkeling at the coral gardens, which was AMAZING. Through Carnival, the excursion would have been $60 each. We got ours for $30 each, and it was great. The only thing I would say is if you don't do an excursion through the cruise line, make sure you get started on your activity early in the day so you don't miss the cruise ship. Always allow plenty of extra time in case of bus breaking down, etc. We allowed 3 hours extra time, and it was plenty.
Tiny closet- Loud hallways.