And both Belize and Roatan have monkey parks.... so you should be set there!
Sting Ray City, Cave tubing, snorkeling and Mayan ruins are the normal tours for those ports... with kids though, you may want to skip the ruins and do those once the family is older. Follow Penny's advice and search our Caribbean port area you can get a much better idea of the things that are available and what to expect at each of those ports. We did the Valor cruise in September and its a great its a great cruise, you picker a good one for your first cruise!
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