I have travelled to Coz dozens of times over the years, usually solo, as my husband is a non-diver. I usually stay at Casa Mex. In addition to the morning 2-tanker, I often schedule an afternoon dive/night dive, if energy permits. Some dive ops offer a "twilight package" of dives. Casa Mexicana is centrally located, I enjoy walking to local restaurants. I also enjoy chatting with other divers on the boat--occasionally I receive invitations to join them for dinner. I would encourage you to get to know your fellow divers, as well as people at your hotel.
You might consider scheduling a day of cenote diving on the mainland, though that makes for a long day. Take time to see the sculptures along the Melgar. And venture back into the "hood" to visit the local market.
Don't be afraid to "go local". On my last visit this past November, the zipper on my mesh bag broke. I made inquiries as to how to get this fixed locally. That was a fun experience locating a tiny shop, leaving my bag for servicing and picking it up after 6 p.m. Years ago I "lost" my metal pointer upon entering the water for a dive. Locals directed me to a shop where fishing gear/metal was fashioned/serviced. The store owner was able to make 2 new pointers, complete with a small hole for a lanyard, out of a length of stainless steel metal. Funny thing, 6 months after this trip, I returned to Coz and my divemaster had my "lost" pointer set aside for me--he had found it on a subsequent dive. (Thank you Mariano).