I just returned from a week in Cozumel and did my dives with Aqua Safari (including PADI AOW training) and finished with 2 Cenotes Dives.
--Aqua Safari--
They seem to be a good outfit, but other than Iberostar's onsite shop, I have nothing to compare them to. I believe they have 2-3 Large boats that do 2-tank dives in the morning (~8:00am) for $55.00 or you can pay $5 more and go on the fast boat. The fast boat leaves a bit earlier and gets you to the dive site sooner, however it's usually the more experienced divers so I would not recommend it for beginners.
One nice thing about Aqua Safari is that they offer an afternoon dive for $9 if you did the morning dives. It was always at Paradise Reef close to the dive shop.
They also offer a night dive, but only if they have at least 6 divers. I was able to get in the night dive on Thursday, but we did not have enough divers for the Saturday dive. The night dives were also at Paradise Reef.
Other than the Paradise Reef dives, I did the following:
Palancar Gardens, Santa Rosa Wall, San Francisco Wall, Colombia Reef, Dalia, and Tormentos
I believe they will only go to more advanced sites (Punta Sur and Maracaibo) if you can get enough people to go and you have been 'checked-out' by them.
They dive a fairly conservative profile and I don't think you could just 'dive your computer'.
-Cenotes-
My final dive day was spent diving the Dos Ojos and Bat Cave Cenotes with Yucatech (
http://www.yucatech.net). You only need Open Water to do a basic cenotes dive. Was a bit pricey ($130 US), but included ferry ride, transportation, 2 tanks, lunch, and sodas. I also sprang to have the DVD created of the Cenotes Dive for a bit more. Our guide was really nice and I think the 2nd dive (Bat Cave) came very close to being a 'Cave' dive as there were several times I could not see any natural light.
The water in the cenotes was 78 F and got a bit chilly in my 3mm towards the end of the second dive. A nice bonus was the fresh water really helped clean my gear up after 4 days of ocean dives.
Good luck and hope you have a good time