You'll be divided into teams red, white or blue based on where you sit at dinner in the dining room. This means all the activities you participate in could get points for your team. Of course the prize for the winning team is free pizza and bragging rights. It will depend on your own taste which activities you might like to go to or participate in...the names are pretty self explanitory and you'll receive a Carnival Caper each night telling you what's going on the next day.
(Embarkation day there will be one in the cabin for the rest of the day and another one delivered that night for the next day.)
Isla Roatan is by far the prettiest of the ports you will be visiting....great place to snorkel or to zip line. I've also heard Belize is great for snorkeling.
Grand Cayman...Stingray City is a must. Go as early as possible. If there is an excursion before nine take it....then hopefully you'll be one of the first boats to the sandbars. It's a great experience. We've also been to Hell, the Turtle Farm, and done the Island tour. The best though is the sting rays.
I didn't see a zipline listed for Roatan....but I did see some Canopy Tours. Sounds like it might be the same thing. We did the Island tour. Something we tend to do each time we visit a new place. Also contained a boat ride, Garifuna people experience, homemade jelly and humingbirds.
Belize...many say cave tubing is the best there. We went on the Altun Ha Mayan Site and River Wallace tour. We really enjoyed it and I was surprised at the size of Altun Ha.
In Cozumel we took a taxi to the far end of town. Shopped at Los Cinco Soles (I'm comfortable using my credit card there.), and ate next door at Pancho's Backyard. I wouldn't call it a "party" place, but the food is good and consistent from year to year. We walked back towards the ship and looked at some other stores and when we got tired we took a cab back to the ship. I did notice in my papers mention of several dolphin excursions here.