Mexico - 7 nights in Cozumel

I'm heading to Cozumel for 7 nights and staying about a $15 cab ride from downtown. I'm curious if anyone has any recommendations regarding if I should rent a car or simply use taxis. I do want to explore the island some, at least a couple days of the trip. Any thoughts on if I should rent a car or just take taxis?
Thanks!

As you haven't gotten a reply, let me add what little I know (having never stayed on Cozumel, only at Playa Carmen). A car is very useful on the mainland but not on the island; most people don't use it on Cozumel. On the mainland a car is essential to see the sights and avoid the bus tours. It sounds like you plan to remain on the island in which case no car is needed and can be a hindrance.