My favorite "port" is actually two ports, close to each other, Ocho Rios and Montego Bay.
I know a lot of you will disagree, and have no great love for Jamaica, but for me it's a different story.
Living in South Florida, I have a lot of close contact with Jamaicans, at work and on a personal level. Jamaicans are a proud people, just as we are proud of our country, and have a beautiful island to be proud of. They consider Bob Marley to be just a step below G-d, and revere him throughout the island. When a bunch of us American tourits descends on them, and treats them as inferior, in their own home, they, rightfully, take offense and "give it back, Mon..."
When I visit, I give them a big smile, a little Patois, and wear an old, faded, Bob Marley t-shirt. I get treated like a best-friend!
Forgetting the walk up Dunn's River Falls, which is interesting and a "must" on your first visit, there are so many things to see and do, on the island.
The river rafting on the Martha Brae, or Rio Grande, is one of my favorite things to do, in any port. The slow, leisurely, glide through the forest, on a raft built for 2, watching the tropical foliage, birds, and other animals, along the way....
...and the ride from the port, a little over an hour, gives you a look at the "real" Jamaica, as you pass through the countryside, and small towns. You can see the Blue Mountains on one side, and the sea on the other.
If you're a Bob Marley fan, and love his music, you can immerse yourself for a few hours on a trip to Nine-Mile. They take you in a "60's" bus, complete with a roof full of (artificial) fruits and veggies. The inside is totally decorated with "Marley," and the sound system probably cost more than the bus. You then get to tour the homestead of the Marley family, where Bob was born, and spent his early years. Bob Marley's crypt is here, in a specially built "temple." WARNING: As you get off the bus, at Nine Mile, there will be a number of Rastas, selling the "holy weed." They will tell you that you must partake, if you are going to the Marley House....
(P.S. They ask $0, but will take less....)
Next time your in Jamaica, try joking with the native people, and being "fun," and see what happens.