JanaB Welcome to Cruise Chat! Don't let your first cruise stress you out. You have come to the right place for answers.
This post should really be in the Caribbean Ports section of the forum and normally I would move it but since its your first post i will leave it here until you respond so I know you know where to look for it when it "disappears".
Now on to your question- Jamaica- The only "must do" thing there is Dunns River Falls. its one fo the more popular things to do there. IF you are going on Carnival you will most likely be stopping in Montego Bay (Sp?). Unfortunately the falls are at least an hour's drive (maybe more) from that port and really not worth the trip. If you are by chance docking in Ochos Rios then its much closer and then indeed worth it. The Zip line tours are also popular but are a bit on the pricey side. Personally we don't get off the ship in Jamacia anymore. But since its your first time I won't tel you not to. Just be sure to book a ships tour and stay in your group.
Grand Caymans- By far and away the best tour here and something not to be missed is Sting Ray City. You can book a tour that only does that or does the Sting Ray's and snorkeling... The water in GC is crystal clear and the snorkeling is outstanding there so you might consider both. You can book through the ship or you can save a bit of money by booking directly with one of the private tour companies (Captain Marvin's is the most popular, you can find them on line to book) I promise you this will not disappoint anyone in your group.
Cozumel- another great snorkeling stop or maybe just a beach stop. Cozumel overs so many choices you may want to split up.. There are Mayan ruins, Jeep drives, 4 wheeler drives, horseback riding, scuba, snorkeling, just sitting on the beach... you name it.. The shopping there is good too, but you can always shop after a tour since most (except the Talum or Chicenitza (wow I can't spell these ancient Mayan names..) Ruins which are on the mainland and take all day.) The Snorkeling in Cozumel (or any water sports) is considered to be of the best in the Caribbean. The recent hurricanes have don't extensive damage to their coral reefs but the water is still crystal clear if you want to snorkel.
Hope that helps.. if you want any further help feel free to ask.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14, Freedom x 2 6/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013