Jamaica is an interesting place. The locals are known for being kind of aggressive. Stories I have heard include people doing things to get you to take a picture of them, and then if you do, they begin demanding that you pay them. We didn’t run into this scenario, but the locals were noticibly more aggressive than other places I have been. We were warned that it was dangerous to wander outside the main port area by ourselves.
Dunn’s River Falls is a classic stop on many excursions, and involves climbing 600 feet up a water fall. It is a lot of fun, and as long as you are in decent shape, it is not too demanding.
We did the Sanara Sail Snorkel & Dunn’s River Adventure, which took us on a tri-hull catamaran. We snorkeled for a while, then climbed the falls. The rum punch they gave us was strong. I think they just added the punch for a bit of coloring.

Here are the ones listed in the Carnival shore excursions book. Not all excursions will be available for every cruise, or during every time of year. Other cruise lines probably offer the same or similar excursions.
Excursions can either be booked through the cruise lines ahead of time, or while on ship. Booking the excursions directly with the operators is also an option. This can save you money, but involves risk if there is a problem.

ATV Adventure (3 hours)
Bob Marley Bus Adventure (5 1/2 hours)
Brimmer Hall Estate & Dunns River Falls (5 1/2 hours)
Certified Two-Tank Dive (2 hours)
Chukka Cove Beach Horseback Riding (4 hours)
Chukka Cova Canopy Tour Adventure (4 1/2 hours)
Zip-lining through the Laughlans River Gorge.
Cool Runnings Sail & Dunn’s River Falls (3 hours)
Coyaba River Garden & Dunn’s River Falls (3 1/2 hours)
Dunn’s River Falls & Dolphin Touch Encounter (5 hours)
Dunn’s River Falls & Dolphin Cove (5 hours)
Dunn’s River Falls & Dolphin Swim (5 hours)
Dunn’s River Falls Jeep Safari (5 hours)
Mountain To Sea Ride & Snorkel Adventure (3 1/2 hours)
Ocean Kayak To Dunn’s River Falls (3 1/2 hours)
Ocho Rios Highlights & Garden Tour (4 1/2 hours)
Ocho Rios Snorkel Adventure (2 hours)
Party Boat & Dunn’s River Falls (3 1/2 hours)
Rafting On The Martha Brae (5 hours)
Gently float down a 3 mile stretch of river on 30 foot bamboo rafts.
River Tubing Safari (3 1/2 hours)
Sailing To Dunn’s River Falls & Beach (5 hours)
Sanara Sail Snorkel & Dunn’s River Adventure (4 hours)
Shaw Park Beach Break & Dunn’s River Beach (5 1/2 hours)
Relax on a beach for 2 1/2 hours, then climb the falls.
Sun Dancer Yacht Cruise (2 1/2 hours)
Super Yacht San San (3 1/2 hours)
The Enchanter Garden & Dunn’s River Falls (3 1/2 hours)
The Spirit Of Ocho Rios (4 1/2-5 hours)
A tour that visits many sites around Ocho Rios.
Ultimate Jamaican Adventure (5 3/4 hours)
Ride a horse, river tube, and hike.
White River Kayaking (3 hours)
Wild Oats Afternoon Sail (2 hours)
Wild Oats Chapagne Falls (4 hours)
Breezes, Runaway Bay Golf Club