The currency in Mexico is the Peso ($). Due to the large influx of foreign investment and tourism, the US Dollar ($) is widely accepted. Always double check your change and make sure that you ask at what rate they convert the dollar for that day.
The exchange rates are the best at the banks but certain banks have a limit on changing dollars for people without bank accounts. Most banks also do not change any other currency than US Dollar, so use the exchange kiosks that can be found all over Playa del Carmen.