In my opinion the ruins in Cozumel are not as grand like the ones in Tulum on the mainland. You might be better off visiting Tulum if you ever fly to the Riviera Maya or Cancun and stay for a few days since you will have more time. The San Gervasio ruins do not reflect the majesty the other Mayan ruins do.
We love going to Cozumel, it is our favorite port in Mexico. Last time we were there I could not decide which beach to visit since some of wanted to snorkel and some just wanted relaxation. I was going to hire a driver for that day so he could take us to several beaches. I was recommended Taz Miranda. He has a Facebook page, and you can message him. Unfortunately for us, we had rain in the forecast so we decided not to go to any beach! As a result, I cannot personally recommend him, but he has great reviews. Maybe you can ask him to take you to the ruins since he will be your personal driver for the day, you might even have time to visit a beach.
If you decide to visit a beach instead of the ruins, I have read good reviews about Nachi Cocom beach. You might have a more enjoyable time since they have limited capacity and you can book online. We used to go to Mr. Sanchos, but it got too big and too crowded.
A restaurant we visit every time we are in Cozumel for the day is Chi, great Chinese food, and their garlic chicken wings are amazing! This restaurant caters to the ship's crew so you might run into your waiter or cabin steward. They have free WiFi if you eat there and that is when we check on the family back in the U.S. It is located in a three story white building across the street from Carnivals' pier. The restaurant is located on the second floor.
https://www.tripadvisor.com/Restaurant_Review-g150809-d1308581-Reviews-Chi-Cozumel_Yucatan_Peninsula.html#photos;aggregationId=101&albumid=101&filter=7&ff=247843415
I hope you have a great time in Cozumel!
