Done all four ports. Belize and Honduras we did in December 2012 and Jamaica and Cayman in February 2014.
Belize and Honduras, I felt both were dirty. In Belize we did a snorkel excursion and went to a private island to lounge for maybe an hour after snorkeling. It was nice, had drinks (paid not included). Snorkeling was good. There was complimentary rum punch on the boat ride back. Belize is a tender port and the snorkel excursion boat picked us up and dropped us off right at the ship. After that we took the tender in and went on a tour of the city. It was on a tram like you'd do at WDW to the parking lots. It really showed you the slums of the area. In Hondarus we rented a private car/drive through Victor Bodden tours. The driver was nice. The tour went to an iguana farm. We then went to see monkeys where we played with them (held them, etc). We then went ziplining. It was awesome, I love 3rd world ziplining. They let you take a running leap off the platform. They let you twist around and flip upside down when ziplining. Some people may fear for the safety of the equipment but a guide always went before us so my worries were eased. The vehicle that we rode in had a cracked windshield and ripped seats. That was the norm to them and the driver thought the vehicle was great. She told us that most homes didn't have running water and the ones that did have running water were mostly salt water so you couldn't use for cooking. So we learned quite a bit about the local culture.
Jamaica/Caymans. We ported in Falmouth, before the cruise this was the port I was not looking forward to the most. I have heard a lot of bad stuff about Jamaica. It ended up being one of our favorite ports. We did the hike up the waterfall, Dunn's River Falls. We had so much fun. The guy was awesome. After that our excursion took us to a place with dolphins to have lunch. The dolphins didn't do a show it was where people could swim with them (we couldn't not included in fee plus not enough time), but you could watch them swim around. The lunch was a buffet and BBQ style food. After the lunch there were places to lounge on the beach (very very small beach) or there were trails. We walked the trails and were able to hold an iguana and see some other animals. Caymans was the port I was most looking forward to on that cruise. Even though I loved the Caymans it was the least favorite port. Way too crowded for me. Everything was packed! We did an excursion that went to the town of Hell, to a rumcake factory (it was so packed inside we couldn't even go in), the Turtle Farm (neat) and then a boat ride out to the Stingray Sandbar (neat as well). Even walking around intown was crowded. Next time I go back to Cayman I will go diving. Should be a little less crowded, as the tour we did was the most popular. I think there were 6 ships in port when we were there (tender port) so that's why so crowded.