You can get a taxi cab anywhere in Cancun. You can take a taxi to the airport, but taxis are not allowed to pick up passengers there [there is an airport taxi system]
Taxi rates are set by how many “zones” you travel through to get to your destination. There are no meters in the cabs. This way you can get a price up-front from the driver as to how much the fare will be. Rates are posted in most hotels near the front desk.
Taxi rates are more expensive from the front door of your hotel than if you walk to the street and flag down a taxi [hotels get a kick-back].
There are numerous car rental agencies for you to choose from. For more information including links to car rental agency web sites see:
Renting A Vehicle
The cheapest way to get around is by public bus. The public bus system operates 24 hours a day, 7 days a week everyday of the year.
For more info see:
Cancun Bus System
For bus travel outside the hotel and city zones see:
Some hotels rent bikes. You can ride on the sidewalks on Kukulcan Blvd. but we don’t recommend riding on the street. We have also never seen “locks” supplied with bike rentals so it is hard to visit a mall without leaving your bike unlocked.
All we can say about renting a moped is that if you do you are risking your life. Those things are death-traps. We have seen the damage done.
There is an Eagle Riders in Cancun where you can rent a Harley and ride up the coast and hit some pretty secluded beaches. We don’t recommend heading into the jungle.