I would eat at Dzul Ha as well. Their prices are reasonable and their food is good. Their drinks are icey cold. Use the afternoon to see the east side beaches. They have a personality all their own.
Evening is in town for dinner and shopping.
North of the plaza on the ocean side street is Cinco Soles. It's kinda like a Mexican Pier One. If you want a more Mexican shopping experience, get away from the plaza and you'll find better deals. Same products, yet better deals off the beaten path. Cozumel is totally safe to wander away from the tourists and the lights.