Cruisette.. just saw this after replying in the Carnival Cruise lines section....
I would not recommend trying to do anything in Jamaica with a private tour. I would stick to the ship sponsored tours. Dunns river is a tour you can get from Montego Bay. Its much more expensive than if you sail into Ocho Rios because its is right there for Ocho Rios where it is a very long (almost 2 hours) bus ride from MB... It is impressive. I have never been to Anne Hall House.. I have heard good things about it though.
Deep sea fishing can cost $400 a person. You can probably book a private tour to take you for less than that but I can not recommend any particular tour. You can also do this in Grand Cayman, but I would do Stingray City in GC. Its a must see. Captain Marvins does a great job, I would recommend them if you don't want to book through the ship.
There is so much to do in Cozumel its hard to give you the "one thing". We have been there 5 times and have not repeated yet...
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