In Jamaica you are doing one of the payed tours, which is good. Jamaica is very interesting to visit, but from what I saw, it is not advisable to walk about on your own. There are some gift shops at the Mo Bay ships terminal where I purchased some souvenirs. Try the Blue Moutain coffee! From what I have heard, Dunn's River falls is very nice.
In Mexico, the Myan ruins at Tulum is quit interesting if you are into history. it is hot, so take water if you go on that trip. I found some great shopping deals around the Mexican ports.
In Grand Cayman, the snorkel with the stingrays seems to be well loved. While there I did an island tour("sea & see") which includes a trip through "Hell", a glass bottomed boat which passes over at least 2 shipwrecks and some lovely corals,and the turtle farm.
Hell by the way is a town, not you know where.
Grand Cayman is also a very nice place to shop.