This place is next to Chankanaab and has good snorkeling, private cabanas.
https://thecabanabeach.com/
I also like Buccanos, they have a great dinner restaurant also.
https://www.buccanos.com/en/activities
Our main hangout for drinks/chill is usually Hemingway
https://hemingwayloungecozumel.negocio.site/#menu
Cerveceria Punta Sur has great pizza and occasionally good beer.
https://www.cerveceriapuntasur.com/
Pescaderia San Carlos for fish
https://pescaderia.restaurantwebexperts.com/
Casa Mission is a little more touristy, but they have good food and traditional atmosphere. I used to live about 100 yards from them.
https://www.casamissionrestaurant.com/
I'd recommend boat tours to Isla Pasion, Cielo and maybe a walk through of San Gervasio.
My old roommate Lucy has lived in Cozumel for 5 years, speaks fluent English, is a certified INAH tour guide and can arrange anything you need, if you're interested.