Years ago (back in 2000-2001), I worked for Celebrity Cruises and used to port in Cozumel every other week for 26 weeks. They've changed the town a lot since I was working there, and some ships now actually get to port at a downtown pier. We used to port at a terminal outside of downtown, about a 5 min cab ride (or a decent walk) to the south of downtown.
We (the staff from the ship) used to go to place called The Reef Club. Since we ported at the terminal that wasn't downtown, it was in the opposite direction that all the guests were traveling. They used to have a daily rate for visitors, and better a deal for us on the ships ($10 a day, all-inclusive). It was also rarely busy, even though we were going during November to May. Now, with all that being said, I don't even know if it is still in business, or if they still offer a day rate.
It wasn't that far away, but was a decent cab ride. I assume that you're going to have people to split the ride with? It's far enough away that you should arrange a time to be picked up by your driver when he's dropping you off.
Anyways, have a good time. Oh, and if you port downtown, have a drink at Carlos & Charlie's before you get back on board. You may not be looking for a party, but this place is a lot of fun, even in the middle of the afternoon.