Since you're going to be in MoBay - eat at least once at the Pork Pit on Gloucester Avenue. It was just a small local jerk pork joint when I first starting going to MoBay. It has grown but the food has remained unchanged - great jerk chicken and pork. There is also Jimmy Buffett's Margaritaville and Sir Winston's Night Club in the same area.
If you are interested in local history then I recommend a visit to Rose Hall Great House on the outskirts of MoBay. It's the remains of the Rose Hall Plantation owned by Annie Palmer in the 1700s. The Great House is reported to be haunted (didn't see or hear ghosts during my visit). Annie was a witch and reportedly killed 3 husbands, burying them close to the beach under 3 palm trees.
In Kingston, visit the Bob Marley Museum. Prices are listed in Jamaican dollars but it is $10-12USD for adults.
Hope you enjoy your trip and travels around Jamaica!