I was there just about a year and a half ago with my Girlfriend and her father. Stayed at Air BnBs in Playa del Carmen and Tulum, and then spent a day in Cancun going around town to markets and the beach. We never had a problem of any kind. If you are at a resort and don't want to be adventurous, just stay at the resort. Most of them have everything you need.
Only drink bottled water, don't get drunk while away from the hotel, and don't attract unnecessary attention to yourself.