You are so close to Hidden Worlds & Dos Ojos, great caves & cenotes for snorkelling. Same for Aktun Chen, which also has a monkey preserve. Other great cenotes include: Gran Cenote, Cenote Carwash, and Cenote Calaveras on the road toward Coba (but very close to Tulum) and Cenote Escondido and Cenote Cristal just south of Tulum pueblo on the highway toward Carrillo Puerto (again, just outside the pueblo, very close to Tulum).

Xel-Ha is close-by, about halfway between Akumal and Tulum. You can get there by taxi or colectivo. You can do it all here: Snorkel, tube down the lazy river, jump off a cliff, swing on a rope, hang with the iguanas, swim with the dolphins ($). You can choose to pay the simple entrance fee, or the all inclusive fee that includes meals and gear.

Archaeological sites

You may also want to check out the ruins at Coba, which is about an hour and 15 minutes from Akumal. There are a variety of companies that will take you, some combined with other activities like visiting a Mayan Village, Zip-Lines, Rapelling, Kayaking, Cenotes, etc. Or you can hire a taxi to take you there independently.

The ruins at Muyil are much less visited than the ones at Coba and Tulum. They are hidden in the jungle and really magical.  They are right off the highway, only about 15 minutes south of Tulum. This is a great half-day trip. The easiest way to get there is by rental car or taxi (you can arrange for the driver to wait for you).  You can enter the Sian Kaan Biosphere reserve from here (for a small additional fee) and follow an easy path to observations towers with views above the treetop canopy and of Laguna Muyil.