We've been to Cozumel 5 times via cruise ships.
There's a really nice restaurant located next to the sea turtle exhibit at Xcaret. You can see it from the snorkeling pool. Has a big thatched roof and a wonderful view. Good food and reasonable. Be sure and order the large margaritas. They're served in the 2-hand glasses. We spent 6 hours there and didn't see it all.
You can take the ferry from Play de Carmen to Cozumel about a 30 minute ride. Drops you off in the middle of the shopping district. Fat Tuesday's is not far up the street to your right. Not much shade at Tulum, and there's an extra charge of around $10 if you take a video-cam, cameras are free. We've enjoyed our visits every time.