Hi Elaine. Welcome. Cozumel is beautiful. The beaches are clean, the water crystal clear blue.
We have always rented a jeep and gone it on our own. We have never encountered any trouble. Steve is correct. Locals drive a little nutty. Excursions organized through the ship are good too. It's your call. Our family likes doing Cozumel at our leisure.
BTW... Chankanaab National Park is a great spot for snorkeling, enjoying the beach or for swimming with the dolphins.