I guess I am more fond of Grand Caymen than Dave is. While I agree that if you are not a snorkeler/ scuba person it does not offer much more than the typical shopping interests, we LOVE the beach there. Stingray city is a much for anyone's first time there. We have booked on our own a couple times (we prefer Captain Marvin's Water Sports) you can get tours for less than the cruise line will charge you and you can get tours that offer both a visit to the Stingrays and a reef snorkel.
Cozumel is also a favorite for water sports. To answer your question, snorkeling off the beach can be hit or miss since the big hurricanes have really damaged the close to the beach coral and there is not much to see. If you want better viewing you need to get on a snorkel tour boat. Most of these can be booked online by yourself. Or you can do any of the beaches by yourself, just work your way out to the taxi area where you will find a sign with the various beaches and the cost of the taxi ride to them. Since you have a decent sized party, you could negotiate for a day trip to a resort, just tell them you are looking for a day pass at a resort and they will help you out. HAGGLE on the price. If you have a big enough group they should be able to get you transportation and use of a resort for $20 to $25 a person. DO NOT book from the "timeshares" sales huts on the end of the pier. you will over pay. (And most likely get stuck listened to a timeshare pitch) Go out of the port area where the taxis are before you start trying to find a place. Cozumel is easy to get around in. Unless you want to do a major Mayan ruin tour, you can book stuff by yourself.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013