It's been almost a year since I've been there, but Casa del Mar had a couple options for diving. One is Del Mar Aquatics, which was their house op, but for the last couple years or so, they've had a "dive concierge" down on their pier which services 3 different ops. I think one was Pro Dive, another was Dive Paradise, but that changed, and I can't remember the 3rd. A taxi from Casa del Mar to "downtown", it's 80 pesos, or about $7us one way for 3 or less people. CDM let's you use the pier for pick-up without charge. They also have dive lockers that you can use with your own paddle lock.
It can be a good option as it's small, has a little bit of "resort" feel and isn't too far from town. For a short trip, you could eat at CDM one night, eat at Ernesto's across the street one night, eat downtown two nights and at Paprika one night. Another plus is the shops that leave from the caleta, but will pick up at CDM, which is about the same as the Park Royal and El Cid which are just north of the caleta. Lunch at any of those places works too, for a short trip.
If you can find a way to do it, you should go for a week. You've already spent the airfare and are dealing with the hassle of travel. It's a nice little "schedule" with more package deals on air/hotel and diving. Many do the 5 two tank trips over a week and have a day off in addition to every afternoon. If you like to dive, you're in the right place to do it. For many divers, non dive days on Cozumel are akin to being at Disney World and sitting in the parking lot.