If bars are not what you are looking for, Cozumel has a good beach for snorkeling, and you can shop (till you drop if you like!) in the town. If you dock in town, you can walk to the shops; otherwise you will need a cab. Make sure you agree on the price before you get in!
Belize is best for nature-oriented tours; I'd recommend sticking with the ship's shore excursions here.
Costa Maya also has good beaches, and is closest to the Mayan ruins of Tulum and Chichen Itza. Again I'd recommend going with the ship's shore excursions. Tulum is closer to where you will dock, and has the distinction of being the only Mayan ruins still left on the coast. Chichen Itza is farther inland and is a larger complex.
Check out reviews of these ports on portreviews.com, a sister site to this one.
Have a great time!