Lots to do in Cozumel, but DON'T join the "pier runners". Be sure to keep your watch on ships time, and don't depend on your phone or other device that will automatically update to local time. I've always had a good time wandering around the local shops, and never felt challenged, or unsafe.
Have a great time in Coz!
Marine, Pilot, Singer, Tuba Player, Carnival "Diamond"!