There really isn't any place in MoBay like Negril, but you do have a some familiar choices. There is the Hip Strip that includes Margaritaville and BlueNotes which is a night club in a similar (but different) vein as the Jungle.
Your hotel will have some live entertainment since there aren't live weekly beach bands like there are in Negril. Some fun beach places include Doctors Cave Beach - one of the first major tourist beaches in Jamaica. There is a charge to use the beach, and a couple great places to eat and drink on at Doctors Cave.
Another interesting beach spot is located believe it or not at the very beginning of the airport runway. You can sit and enjoy cold drinks and great jerk chicken while watching the planes come in.
For something completely different, you may want to try the Montego Bay Yacht Club. You do not need to be a member to go to the bar and restaurant. The food is excellent and the view is great if you like a marina setting.
I am sure others will have some ideas - but this should get you started.
