Welcome aboard Jewelbeemon!

During the slow season some places do close, but you certainly won't starve or be bored. Most Jamaican owned places will stay open all summer. Unfortunately, I believe Boat Bar is one of those places that does close (or they at least stop the live music). However, you will still find live music at Drifters, Bourbon Beach, Alfred's and Roots Bamboo. On the cliffs, Sea Star will still have their Saturday night show and I'm sure there are few places I am missing. Of course, there are also the wandering beach musicians who would be happy to jam with your companion.

I am mostly a cliff dweller (and have been to Negril in June and August), but I know for sure places like Connie's Country/Western Pub, Pablo's, Shark's, Sips & Bites and 3 Dives will definitely be open. Also the restaurants in the resorts like Catcha (Ivan's), Tensing Pen and Rockhouse (Pushcart too) will be open. Same for the beach - any restaurant associated with a hotel will be open (Charela, Coco la Palm, Treehouse, etc.).

It's too bad you are leaving on July 8th. There is an event happening at Negril Escape called Roots, Rock & Culture, that has the potential to be pretty awesome:
http://negrilevents.com/event/roots-rock-culture/