We did the "Stingray" City the last time we were at this port and enjoyed it. Other than that though, there isn't much of interest here. Quite a bit of shopping. My wife and mother in law shopped and the kids and I stayed on the ship for the most part and enjoyed some of the onboard activities.
Cayman is a tender port so it takes longer to get on and off - though the tender ride is very short.
Wife and mother in law did cooking class with Josefina (see thread under Cozumel port board) and thought it was fantastic. Josefina told them that they were the first people to do it in a couple of weeks - this is really amazing considering the individual experience. Cost is $80 per person which is about the same as most ship tours - but the experience is much more interesting. Very highly recommeneded.
Kids and I went to Paradise Beach and enjoyed the water activities (slides/trampolines/kayaks/snorkel stuff) ($10/person) and the beach. Drinks all day with some food as well came out to $40. There is a 20% surcharge for credit cards - bring cash. We got there very early and were one of the first ones - got more crowded as the day wore on.
Cozumel has a pier so getting on and off the ship is very easy.
We did the Cave Tubing with "Major Tom" (see Belize port thread) and had a great time. Carnival does not offer cave tubing through their tours (supposedly someone died recently because the water was high and swift and the excursion proceeded anyway - so Carnival does not offer it) but you can book independtly through Major Tom for around $50/person. This is a long excursion - about an hour drive each way, 45 minute walk, and 1 hour and 15 minutes for the tubing. Add in time for getting equipment, etc. and it is pretty much an all day thing. We thoroughly enjoyed it (water is around 73 degrees - so a little chilly but no problem) and were hard pressed to see how someone could have died doing it but maybe it was just an especially rough day. Highly recommended.
We were about 30 minutes late getting back to the ship and believe that we were the last ones on the tender (Belize is a tender port with a rather long tender ride). There was a bad traffic accident on the way to the tubing that delayed us about 45 minutes. We were concerned because we had booked independently (not through Carnival) but Major Tom said he called the ship and they agreed to wait for us - he must have been right because as soon as we boarded the tender, that was it. It was a little nerve-wracking but if you want to cave tube on Carnival, you have to do it independently. It really is a one of a kind activity (my 84 year old mother in law did it with us and she loved it - so how scary could it be?)
This is a port with a pier - so on and off is very easy. We did the "Kayak and Snorkel" Adventure through Carnival and had a great time. Snorkeling is very good here and we enjoyed the kayaking. Very laid back and relaxing.
Be aware that you must be back onboard at 2:15 pm so you are in Roatan a very short time. (about 6 hours) - not time to do too much.