Find the El Pechugon and eat great rotisserie chicken (at least Google says there is one on the island).
Eat tacos and burritos--many choices
Eat at the many great restaurants..
Visit el Museo de Cozumel (their web site says it's closed for renovations)
Learn more Spanish by trying to find someone who's English is not better than my Spanish (not so easy to find).
Find the best deal on dive T-shirts (after the cruise ship people go back to their boats).
Get your picture taken in the Isla Cozumel sign in the park.
Watch the sunset.
Go visit the crocodiles at Punta Sur
Make new friends.
YES! Pechugon is wonderful - on the corner of Av 65 and Calle 11
The Museum is going to be AMAZING when it's finished and will definitely be an attraction you won't want to miss
Have your dive op set up Cenote dives or mainland dives for you
The water fountain show in the mai plaza is pretty neat - every night from 8:00 - 9:00 (it starts off lame, so be patient)
East side is beautiful on windy west side days
People watch at Puerta Maya cruise ship terminal/park
Women - GREAT mani's and Pedi's at KATU in Puerta Maya
Massage with Barefoot in Cozumel Massage: Barefoot in Cozumel
Discover Mexico
Planetarium
Rent bicycles and ride around the island
Go for a walk/run on the waterfront on either side of the island
Rent a Harley
Do a northside tour with Adrian Cozumel
I could continue, but this is a start...