Cancún has mostly "American" style places. Like Señor Frogs and TGI Fridays. All along the "7" there are resort hotels. The Gulf is to the east and north and there is a large lake to the west. Don't swim in the lake. There is a "flea market" area in the resort area so you can buy Mexican chit like trinkets and sombreros. Take a day trip to Tulum or Xelha.
Be smart about your money and valuables, don't get too drunk, but have a good time.
It's plenty safe. Our media makes Mexico sound like the wild west, but it's probably the safest place in Mexico.