Dreams Puerto Aventuras now offers free Wifi throughout the resort including public areas and all guest rooms. They also have a new smartphone app that, when connected to the hotel's Wifi, allows the user to make free calls back to the USA and Canada. 

Aventura Spa Palace has free wifi, as do all of the Palace Resorts.

Catalonia Yucatan Beach & Catalonia Rivera Maya do as well

Most restaurants have wifi, but they will be password protected.  Some have signs with the password listed, other times, you'll need to ask.

The Royal Suites Yucatan by Palladium offers free wifi in the lobbies and in the rooms. The Grand Palladium Kantenah, Colonial, White Sand and Riviera offer free wifi in the lobbies.