You should also check out cozumelinsider.com
It lists all the beaches/amenities in cozumel. We were in Cozumel 1/04 and rented a car through the site (with insurance and all it was around $70, but we had 4 people to spread the cost). We drove south and around to the east side. We stopped at the lighthouse, then off to playa bonita. It was a nice uncrowded beach. We had plenty of room to get our own loungers/tables/umbrellas. We even had a nice waiter bring us drinks!!!
The only thing I would note about the east side beaches is that there are a little more rough than the west side, and there was some seaweed washing ashore. Not the greatest swim, but very nice. Our day was a little overcast, so we stopped at several beaches on the east side. We went to Coconuts, which is on a cliff overlooking the beach below. It is the highest point on cozumel. Really great view & great chips & salsa!!! Not to mention the margaritas.
We ended up at mezcalitos, the last beach on charted roads before turning back to town. They had hammocks on the beach which were great...and, oh yeah, great margaritas! I have to say my day in Cozumel was one of the greatest of our cruise....nothing like exploring on your own...just watch out for the Margaritas...they make em strong!!!!

Thank goodness I wasn't driving!