Belize...Cave tubing or Mayan ruins... best port to do either. Lamanai is freakin amazing! All the tour guides are full of great information and teach you all about the jungle, different plants, Mayan history. Just can't go wrong with cave tubing or ruins in Belize.
Mahogany Bay Roatan... gosh, the island of Roatan has a ton of great excursions, places to go. The reefs are right close to shore so if you want to snorkel, this the place. If you like white sand beaches it is the place to go. If you want to see monkeys and sloths, it is the place to go. And if you just want to stay in port there is a free beach next to the ship, you can pay for kayaking or ziplining right there at port...