Jamaica is truly an exciting place to visit for almost anyone. There is something for every personality. I would say it depends on what you want from your visit.
If you love the beach, there are a few places that you must visit. Dunns River Falls and Negril are two that can easily be googled.
If you love the nightlife (clubbing, bars etc), be sure to visit the hipstrip in Montego bay which has great nightlife. One great place is Margeurita Ville 9 bar with disco, and water trampoline, slides etc. Another great bar is Ricks Cafe which has great sunset views, fabulous drinks and thrilling diving (from the rocks .
If you would like to be involved in culural activites, try to visit during one of Jamaica's music festivals where you can enjoy great reggae music. Google reggae sumfest for more info on these. Also try to visit one of Jamiaca's Jerk spot for great Jamaican food. The best spot for Jerk chicken and pork (really spicy) is Boston beach.
Watersports are also great in Ocho Rios and Negril, and there is swimming with the dolphins at place called Dolphin Cove in Ocho Rios. Another thing you may like is rafting which is well represented in Jamaica. One of the best is a raft down the Black River Safari. All I can say about this is that it is unbelievable. A sure must.
I plan to cover Jamaica for some of my future hubs, maybe you will find other things that I missed if you follow. Jamaica is pretty small, and the resort areas are fairly close to each other, so all the activities I have described should be half an hour to two hours drive apart.