If you take a cruise that stops in cozumel, you have a couple of choices.  If you're looking to party and drink a lot, there are bars such as Carlos n' Charlies and pub tours. However, if you want to scuba, snorkel, relax, be entertained, eat well and generally have a good time for a couple or family, the place to go is Chankanaab. The park is a wonderful way to spend the day. The snorkeling and diving are amazing, complete with underwater park trails. The animals in the shows are treated very well, and the shows are impressive. The walking trail through Mexican history is great. Try the tortillas made in the replica village..

There is some debate about whether or not it is legal to purchase black coral jewelry. Make sure you keep the receipt so if customs bothers you coming back into the states, you can show them what you purchased was legal. Black coral is endangered, and tourists often have their purchases confiscated coming back into the states. Do some research before you leave on your trip or at least before you buy on your vacation.

One further suggestion - the ceviche at the restaurant in the park is amazing. 

Note that it is MUCH less expensive and more flexible to do this on your own vs. a cruise ship tour.  Just take a taxi to the park (make sure to establish a rate before you depart!) and pay the admission.  Then you can take a taxi back to town or the cruise ship.  Get some pesos from the ATM to pay the taxi driver, or you can haggle with US dollars.

Wheelchair Access

Chankanaab is quite wheelchair friendly and most of the non-beach areas are accessible, with flat floors and ramps. Some parts are compacted sand, so the surface is loose, but this doesn't pose much of a problem.

Bathrooms are reasonably accessible, with some support bars on the walls, although the doorways have not been widened.

A limited number of beach wheelchairs are available for free on a first come, first serve basis. They have "balloon" wheels so can be pushed across the sand.