The Conquest is a great ship! You'll have a great time. The only "not to be missed" thing I know of is the Stingray City excursion. You will be amazed. You can book it through carnival (do so ahead of time if you do) Or you can do it cheaper through a private tour company. (You can google on Grand Cayman stingray city tours to find an operator)
Cozumel is a great place to snorkel, scuba dive or just relax on the beach.
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
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013