Summary: The city of activities. From the beach to various local meetups and events to nearby hotspots Cancún and Tulum to day tips to Cozumel, Cenotes, adventure parks, and historical sites this city of only 300k with a constant inflow of visitors could keep you busy for a lifetime.
From the Cancún airport, take the ADO bus.
For Spanish classes, text Ana (+52.984.253.2346) or Agora Language Center. These might be the best Spanish teachers I've ever found (I tested about 10 teachers here in Playa del Carmen alone).