We were on the Inspiration in Dec. 02 and loved Cozumel and Grand Caymen. We did the Dolphin Adventure in Cozumel through the ship, but you can also arrange it on your own via the internet (do a search on Google for Cozumel Chankanaab Park.
As far as Grand Caymen, we rented a car, went to the turtle farm, enjoyed the beach and toured the island. In hindsight, we should have swam with the stingrays at stingray city. Our ship left very early in the day (about 2:30 p.m.) and we were unable to arrange a trip to stingray city on our own. Either have it arranged prior to your trip, or take the ships excursion.
We have been to the Carribean many times and those are two of our favorite islands.