I did not see anyone mention a dive at Playa las Casitas, did I?
It's a great shore dive in Cozumel (compared to what else is available, that is). Enter the water at Cafe del Mar (roughly across from the naval base). As you swim from shore make a heading towards the buoys. Note the current strength and direction.
After Hurricane Wilma, the large chunks of concrete removed from the destroyed Puerta Maya pier were placed in this area to create an artificial reef. This was in 2005. To date there isn't much growth on them. It's mostly just an odd experience seeing large square chunks of concrete in the water. Anyway, swimming past these concrete chunks you can reach the shipwreck of the Laguna de Mandinga, an 85 foot (26 meters) long Mexican navy patrol ship. It sits in about 40 feet of water and is positioned with her bow pointed north. It is marked by two mooring balls; the stern, is marked by a red ball, and white mooring ball is attached to her bow. There is starting to be decent sponge growth on the ship, and lots of "critters" have settled in. On my last dive here I found a large sea horse swimming across the open sand just east of the ship. At the stern of the ship is a pile of rubble rock.This is the old section of Paradise Reef that was removed to make room for Carnival Cruise's pier at Puerta Maya. I believe the rock was moved here in early 2014. It has solid growth on it. Drifting past the rubble brings you to a second shipwreck, the Laguna de Pátzcuaro. It is/was a 42 foot Mexican patrol boat.
I should note the current here is most often running north to south (different than the typical Cozumel south to north current). At times the current can be STRONG. A strong south current can push you into the travel paths of the passenger ferries. Thus make sure to use compass headings and head towards shore once the current has blown you past the second ship. Once off the shipwrecks / artificial reef it becomes mostly sea grass so no reason to hunt for more structure. Also do not make this dive without a large, bright surface marker buoy. Did I mention strong currents are possible?