Plenty suggestions depending on what you're into. The island is pretty small...my best bit of advice on how to get out and experience the island is to step just outside the resort and find a friendly taxi driver. You can haggle the cost to where you hire the driver for the day, and he will show you around the country. It definitely beats hopping on the tour bus.
If you head toward the other side of the island at all...there are some must-see spots in Ocho Rios. Fern gully is an amazing rainforest tucked in the hills just South of Ocho Rios. The drive alone is worth it...but there's also a crystal clear stream running through there with hundreds of colorful FW fish along the shallow banks. Also check out Dunns River Falls if you head that way. But...don't drive straight there. Ask to be taken to the other side of the bay across from the falls...then hop on a glass-bottom boat. They will take you across the bay to the base of the falls, and while you are in that bay on the boat you pass over a beautiful coral reef just below the surface of the water. It's pretty incredible. The hike up the falls is intense in spots...but doable, and there are guides to show you the way up.
For a more touristy must do...check out Pelican bar in negril. It's definitely a unique experience.
Ask away if you have specific questions...it's been a handful of years since I've been back, but technically I'm a dual citizen so I know my way around