We have dived three cenotes as part of a dive trip in the Cozumel/Playa del Carmen area. Dos Ojos, Carwash and Gran Cenote.
This whole part of Mexico has this huge network of underground rivers called cenotes and a large number can be dived without needing a cave diving qualification. Although you can go from Playa del Carmen, Tulum is better because there is no ocean diving to speak of so all the dive operators in town specialise in cenote diving, and many of the good ones are only a few minutes drive away.
A quick look on Google images will give you a good idea of what to expect. Provided you are OK with confined spaces, although some of the caverns are huge and you have good buoyancy, I would recommend this to everyone. Even poor air-consumers are fine because the dives are relatively shallow (rarely more than 15 metres) and the water is still, the dives are really gentle. Strict rules apply to those that lead the dives, which are actually treated as cave dives in terms of redundant gear, even though they are not. For non cave divers you will always be able to see the surface even though it may be up to 60 metres away. Visibility, subject to the amount of available light is to all practical purposes, unlimited.
Because the dives are shallow there is little in the way of surface interval, so by the time you have driven from one cenote to the next and kitted up, you are ready to go again.
One other thing; because the water is so clean (it's effectively spring water that has filtered through the limestone) your kit will be cleaner at the end than at the beginning and will be ready-rinsed.
It is the wet season between August and November and it can be very wet apparently. We're here in June which is off season but that is all plusses for us, it's quite (we were the only divers with the guide today - they are allowed a maximum of four divers) yet apart from the occasional shower it's been continuous sun. But this is proper heat 38 degrees C.
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