I would not take a newly certified diver into the cenotes, for a number of reasons. The biggest one is that you don't have any idea how a newly certified diver will cope with a problem while diving -- If a mask floods, or a regulator begins to breathe wet, and the diver bolts for the surface while in an overhead environment, you have a recipe for an accident. Second, the cenotes are a very fragile environment. Unlike a reef, where healing may be slow but is going to occur, the caves will bear the marks of our errors in buoyancy and positioning forever. I think the cenote dives are absolutely fabulous, but I think people ought to wait until they have the experience and the skills to do them safely and with respect for their beauty.
Diving off the mainland is somewhat different from diving in Cozumel. You don't tend to have the 100 foot viz, but you may have more larger animals (turtles and sharks, for example, and tarpon). I haven't done any open water diving from the mainland, but my husband has, and he enjoyed it. Given the hour's drive to Playa from Tulum, and the need to find parking and hike gear to the ferry, the half hour ride across on the ferry, and the fact that most Cozumel dive ops go out fairly early in the morning, I think it would be pretty reasonable to sacrifice the viz for a much more convenient dive experience -- unless you were planning on going over and spending two or three days on the island.
I can recommend Aquanauts in Puerto Aventuras as a dive op. My husband has been out with them, and thought they ran a good operation, and he enjoyed it.
