OK, tough questions because there are three absolutely correct (i'm highly biased) answers.
Diving the Cenotes with Cenotexperience is never a wrong choice. Great guys and maybe the best divers I have ever seen. Cave divers really are amazing. I usually try to spend my dives copying every move Martin makes...and usually fail miserably. Even then I become a better diver.
If spending the night in Coz is not an option for whatever reason, if Cenotexperience has an option to get you to the reefs, I would take that as option 2. Just a great dive shop.
Option 3- There are many cheap options for lodging on Coz. From a $12 hostel to $40ish a night hotels such as Suites Bahia. Villa Aldora is probably more $$ but has a dock that they will pick you up about 100 feet or less from your room, make sure to snag breakfast in town when you arrive. Hotels.com will show several options within walking distance of the Aldora pier in town. Take the evening ferry over, spend the night, and dive the reefs with Aldora. Sherief and (Little) Jorge are my favorite DM's but you really cant go wrong. Wake up, hit El Coffee Cozumel for a double expresso and a pastry on the way to the boat, go do 2 dives with steel HP120's for stupid long dives, enjoy some of the best diving in the Caribbean, and when you get back hit The Thirsty Cougar (Green/poblano chille chicken burrito and a Bohemia Obscura), Quatro Tacos (They have about 6 normal menu tacos, usually one special, and great guacamole...you cant go wrong), Lobstershack (their version of a lobster roll), or walk to the square and hit up Casa Denis for the Sexy Shrimp, its not on the menu but ask for it anyway. Since you are in the square...walk back to Michoacan for a plain vanilla ice cream bar. Once you are fed and hydrated with several Bohemia Obscuras, head back to the ferry and catch a nap on the way back.
I would lean towards option 1 or 3, preferably both over several days. I usually dive cenotes at least once on every trip...but the morning ferry has always been an option coming from Coz.
Good luck, Safe Travels, please drink several Bohemia Obscuras for me.
Jay