First off - where are you staying? In the hotel zone in Cancun, at an AI along the Riviera Maya, Playa del Carmen? It's all important as to access to things to do.
As far as a generic list-
Mayan Ruins- Chichenitza is cool but an all day, hot as bawls, slog. I prefer Tulum as it's right on the beach and has some very cool ruins. Plus the town of Tulum has some nice restaurants.
Dive a Cenonte - there are lots of them. Pick one close to where you are staying.
Xel Ha water park - fun, lazy river float and just cool spot to spend a day.
Snorkle/booze boat out of Puerto Adventura
Our preference in terms of a town in the area is Playa del Carmen. We have stayed in Playacar, the resort area just south of town several times and we just really enjoy all the restaurants, bars and general "scene" along 5th Avenue. If you are staying in the hotel zone in Cancun itself the local shuttle bus is a couple of pesos and runs continuously past all the hotels and goes into town so there is no reason for a car. Likewise, if you are in Playacar its a short taxi or walk to and from 5th Ave and the hotels. Anywhere else you might want a car as you can feel pretty isolated at some of the outlying AIs and taxi rides can be $40/$50 each way into towns.
Have fun, until I bought some land in Cabo and am building a house, the Riviera Maya was our favorite area to vacation.