I went on a cruise a few years back that stopped in Cozumel and I had a blast! From my memory (and their website) they claim that all served water products are either purified or bottled (ie drinking water, ice, vegatables and such washed in purified water). I'm not sure about water out of the tap though. One of the places I enjoyed most is not on mainland Cozumel, called Xcaret. Lots of stuff to do there, beach, underground river, swim with dolphins, old ruins (maybe mayan?), scuba/snorkle, golf, great food, and a few bars, just to name a few things.

Have fun!