Circumnavigating the Island
It is possible to drive all the way around one half of the island of Cozumel. The island has a road bisecting the island into Norte and Sur halves. The coastal road that allows you to drive around its perimeter is known as the Quintana Roo C-1.
Why would I want to do this?
I don't know, but it is a thing that can be done.
Are the beaches different or something?
Yes, there's that. The Eastern coast's beaches are way more wild, rocky, and unprotected. Big waves that do not entice a swim. Pretty incredible views, though. A lot of it looks like pastoral paintings.
Anything to do besides look at the ocean?
Yes, there are two restaurant bars on the Easter coast that are worth a visit.
Coconuts
This is the beach bar you go to in your mind when you think about hiding out on a beach in Mexico. It has character and charm. It's a glorified shack with $4 cold bottles of bear, a decent fry cook, a few local favorites, a couple parrots hanging around talking at you, and hammocks on a cliff overlooking the ocean. I didn't want to leave last time. Should have just taken a cab there for the afternoon.
El Mirador
More than 2000 Google reviews, and a 4.6 star rating. Note how many reviews wished they had planned to stay for a few hours. Honestly, this one is worth a cab ride just to hang out on an off day for something different to do . Incredible views, great seafood, great tacos, and a great bar. Definitely a bit pricier than Coconuts, but it's quite a bit more refined.
The Mojito Factory: Welcome to Miami Cozumel
This is a tiny bar with simple seating, great views, and one model: Fast, inexpensive mojitos. Best mojito I've had.
Freedom in Paradise Reggae Beach Bar & Grill
Finally, this Reggae Beach Bar & Grill has been run by a couple of Rastas for a couple decades. They bring the Jamaica beach vibe to Mexico. TRhe paint and decorations are over the top, and the wind at this southern point is steady and strong. But the vibes are great, and it's close to the eco park.
Crocodile Sanctuary
On the way to the southern point of the island, Punta Sur, there is a national park and reserve featuring a massive lagoon system filled with Crocodiles. There is an observation point where you can look out and see them. There's a walking path and tower as well where you can see the animals in the water. I honestly wouldn't recommend getting out of your vehicle any other place near that lagoon.
Faro de Punta Celarayn
A bit further past the crocodile sanctuary is the lighthouse at Punta Celarayn. It is a historic lighthouse open to the public for climbing.
This is as far south as I would adventure on this road if you are driving yourself around. The road can get rough, and you are probably in a rental. Head back north and catch the C-1 west again.
Bonus! Race for the Gas Station!
You've probably been out all day, and you really couldn't resist catching the Sunset at the Eco Park. But now the sun has set, and you are still a good 30 or 40 minutes from town (if you follow the speed limits). You aren't gonna make it before they close. Just turn on into the resort when you get to it. Just consider calculating the fill-up fee into the rental cost.
***Hail Mary: There is one possible hail mary solution to this problem. You can get up real early, race into town, fill up, and race back before the rental car place comes to pick up the car. This is a risky move, but I have seen such a caper pulled off successfully.