Casa Cenote is before Tulum and doesn't charge and entrance fee. Other popular cenotes are Gran Cenote and Ponderosa. Watch for signs along the highway. If you are a certified open water diver, you can dive in a cenote cavern with a qualified guide. Anyone can snorkel or swim in a cenote, but you should never dive in a cenote, cavern or cave unless you are certified to do so or have a certified guide with you.
People die from scuba diving in caverns and caves without training.
See the National Association for Cave Diving or the cave diving page for more information. You can see the inside of some caves without getting wet. Just South of Akumal is Aktun Chen, a dry cave you can tour. There is a sign for the cave on the right, and a large sign on the left for DIF, a government run camp. Take care of your ears after swimming so you don't get sick.