Thanks for this thread. I'm always looking for new shore diving places. My favorites so far are Blue Angel, Dive Paradise and Aqua World
Blue angel offers easy in and out (either on the sand/rock path or giant stride from the pier). I prefer jumping in off the pier. Fell on my butt once on a rock when I slipped trying to walk on the sandy/rocky entry and had a good bruise for days. Didn't hurt though. The dive shop is very accommodating, friendly, and more than willing to help with whatever you need. If I remember correctly, tank and weights was $10 for the day. I put in at Blue Angel and usually drift to the caletita just short of the ferry pier. There is a lot of life along the way, especially if you swim out from shore to the grassy area. Take a flashlight. Every nook and cranny will reveal some marine creature. The fileclams are brilliant red in case you haven't noticed. I get out at the sandy caletita and walk on the sidewalk back to Blue Angel in full scuba gear. This gets a few stares but is SO Cozumel

You can also go south beyond the stingray pens to the grassy area. Here I find many balloonfish in the eel grass. And immediately around the stingray pen there are lots of critters residing in the bricks and fencing. Blue Angel also offers good meals, and lounging chairs if you want to catch some rays or rest before heading to your next Cozumel adventure. Pool is for guests only.
Another favorite is Dive Paradise across from the Hotel Cozumel. Rent tanks and jump in off the pier, or enter gently through their ocean pool--there's a little hole in the wall and this is easy entry and exit. The wall there is loaded will thousands of sea urchins, and there's lots of marine life in this area. Gently swim against the current along the wall for a ways, and then come back. This wall also has big rock formations that hold tidal pool-like marine life. Great place for photographers.
Have also night dived the shore at Aqua World (across from the Grand Park Royal Cozumel). Going south towards the cruise ship pier it gets deep. I saw more octopus and squid on this dive than we could count.
On shore dives, the current is usually not as strong as on boat dives so there is more opportunity for photography.
Before you short dive anywhere, be sure there is easy in and easy out. I cannot exit on iron shore. If that's the only way to exit, I don't do it. Just FYI. YMMV. Happy shore diving

You'll be surprised at how much there is to see.