Went cave tubing in Belize. It's a 5 mile tender to land and Carnival tells you, if you don't have an excursion planned, don't leave the secured area. Any excursion will result in a long bus ride. Our was about 1 1/2 hr each way. You do get to see a lot of Belize that you normally wouldn't see. I'm glad I did the excursion but next time I might just go to port for some shopping and then back to the boat to play in the water park and pool.
We have been to Cozumel several times. Nice beaches there and really good shopping. Both in the village where you walk off and downtown, which is about 3 miles away. You can take a cab there for about 10 bucks or make the walk. A lot of shopping along the way. Plenty of places to eat and drink along the way
Mahogany Bay is a great beach day. Walk off the ship and enjoy. Take the chair lift. It's an easy walk to the beach but the lift gives a nice view. There is some good shopping there also