Greetings and salutations, Maryannb... I am not trying to pry whatsoever. I am just wondering if anyone you are travelling with is capable of driving a jeep. All of the island's hotspots are easily reached with a jeep and the rental fee would be much less than the taxi fare. The main "highway" is basically a circle around the island which makes is american-proof. As far as an answer to your original question, I have no idea. I have visited the island on many occasions, (pre-hurricane and post-hurricane) and I have always secured my own private transportation.
maryann, I'm with dr on this one. We always rent a jeep and sightsee Cozumel on our own time frame. It is nearly impossible to get lost in Cozumel, jeeps are reasonable(approx. $100 for the day), and you can take in the beauty of the island at your leisure. A taxi may run you more than renting a jeep.
Dwayne, we never pre-book with a rental agency. There was never a need to. In Cozumel, they never ran out of cars to rent.
You will be greeted by car agency reps. as soon as you disembark. They are always holding car rental forms attached to clip boards. These guys are easy to spot. We ask each fella their daily price for an "open" jeep. After we get a price from every well-known agency, we decide who we rent with. It takes only a few minutes. I believe we went with Avis last time. Make sure you tell them if you have AAA. They do discount a bit for it.
For our family, it's freedom and there's no safer place to go it alone, than Cozumel, in my opinion. What the heck... take a chance. Columbus did!