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.
Cozumel: We went to Passion Island on the Twister boat (booked through Carnival). The Twister boat was probably my favorite part, but the beach was very pretty. The port seemed really cool too, but we didn't have a lot of time to explore it.
The food on board was delicious- they had many options (buffet style comfort food [included in the cost of the cruise], Mexican food restaurant[included], a burger restaurant [included], sit down dining [included], steakhouse [not included], cafe [not included]... you get the idea). Some restaurants were only open at certain times, and you had to reference the agenda (delivered daily to your rooms)to check those times.
The entertainment was great, but it seemed like most of the "good" stuff was clustered in the evenings, making for some sea days that were hard to fill.
They had some very funny comedians (2 comedians would typically give 4 shows each night- they would each put on a family friendly show, and then an adults only show). The family friendly shows were the best. They were very funny.
They also had some broadway revue shows--the singers and dancers were fabulous, but the clothing and dancing was very suggestive. I would say that it's not appropriate for children.
The service was inconsistent. By that, I mean that our housekeeping/steward service was AMAZING but the sit down dining experience was very poor. We had the early dining that started at 6:00, and every night we got our main course after 7:00. We usually had to allow two hours to finish the meals, meaning we couldn't go to any shows that were before 8:00. The dining service was slow and sometimes a little rude, which is sad, because on our last carnival cruise we loved the service. I guess it depends on your waiter. At the end of the cruise, we adjusted the gratuities accordingly. They put in the tips automatically, so if you need to make them more or less (depending on your service), just go to the guest services desk before the last day of the cruise. It was very easy and they just gave us cash back.
We made the mistake of getting a stateroom on the first floor, which was bad because the Lido deck was on the ninth floor (and the Lido deck has most of the food, entertainment, etc.) The elevators are not express, so it will take FOREVER to get up.
The fitness center has tons of equipment and does offer classes. Some classes are free (morning stretching and abs class) and others you have to pay for (yoga, etc.)
All in all, I think this will be our last cruise. The ship was crowded, with too many parents who did not keep track of their kids (making for loud and obnoxious, unsupervised children). The food was tasty, but during peak times the lines were long. The destination cities were the best part, and I wish we had more time in some of the ports!