Schedule a guided tour and snorkel in one of Mexico's many underground cenotes nearby.
Hit up one of the beaches in town. There is beachfront space at the Grand Hyatt, but outside the hotel, there are many options like Parque Los Fundadores or one of the beach clubs.
Try the best restaurant in PDC, Axiote Concina de Mexico! For other restaurants, check out Calle 38, which has other great options like La Cuave del Chango and Amate 38.
Take a glass bottomed boat to Cozumel. The port is within walking distance of the hotel!
Stroll this pedestrian-friendly street, called La Quinta, where you can people-watch and shop.