We rented a jeep in cozumel last year and had a great time. Trish may be right, but I would disagree. I don't think there are carjackers, etc., in Cozumel. Insurance is different, but we decided to chance it. People drive fast in the downtown area and maybe near Chakanaab, but otherwise, the roads were almost deserted.
We drove first to San Gervasio ruins and spent some time there. We hired a guide -- I would recommend not doing that -- it will take you too long and we couldn't understand him. I'm glad we stopped, but would not hire a guide again. I was glad to see the ruins, but we took too long there.
Continued on that road to the other side of the island and drove the whole length (not that far) stopping at a few places along the way. Again, not much traffic. That ride was very enjoyable.
We came around the island and snorkeled at Dzul Ha. It was okay, happened to be a lot of jellyfish the time we were there. We also had a drink and some lunch there. This year we're going to stop at one of the other places, Mr. Sanchos, Nocci cocoum (Sp?) or someplace like htat.
We were a little rushed turning the jeep in because our ship left a little earlier and our girls wanted to spend some time downtown. So some of your decision may depend on how long your ship is in port, too, on how much use you will get out of it.
Check out cozumel websites, there's lots of good info, like, there are only 2 gas stations on the island, etc. We waited to rent until we got there. It was not as easy to find rentals as I had imagined and we ended up renting from Hertz which was okay and probably about same price as others. This time I think I'm going to reserve in advance and we may do a VW convertible, just a tad cheaper.
If you go the route of renting a jeep I think you'll be happy and have no problem.
Ok, i've rambled long enough - have fun whatever you do.