I say this not knowing what shape Cozumel is in after Wilma. We left there on the Sun just hours before Wilma slammed ashore. Quite an interesting trip (you might want to read the review in the Readers Review section)
But, back to Cozumel. My favorite thing to do is catch a cab and go to Chankanaab Park. Depending on which pier you're docked at it is $6 - $10 for the cab (per cab, not per person) then admission is around $10 or so. It's a great beach with places to rent snorkel gear, a couple nice little restaurants and a swim with the dolphins feature for an additional price.
Restrooms are clean although there is only cold water in the shower.
A pretty lagoon for wandering around (can't swim in it) and a nice botanical garden.
Or if you prefer the drift snorkeling excursions are nice too.
In Belize I'd recommend snorkeling on one of the offshore cays. Don't remember which one NCL offers but it is beautiful water. I remember the corals being so plentiful and huge. More so than other places I've snorkelled.