Costa Maya has a dedicated cruise terminal with shopping, bars and restaurants. DI has at least one shop there, there's the standard t-shirt/souvenir shops, other jewelry stores, 'native' crafts [sometimes made in China], et cetera. One of the bars has a swim-up counter, and as if it now needs to be said, there's a pool [large, chlorinated]. When we were there three years ago, there was a guy with a large splotch of canvas and umpteen cans of spray paint painting veryvery detailed Mexican landscapes. My wife bought one and it's hanging in the family room.
You can wander in this area the whole time there and probably not get bored. Or you can leave the terminal area and go out into Mexico proper, and catch a cab, rent a bike, or simply walk the mile down to Majahual. Majahual is a tiny little fishing village which probably holds the Mexican patent on "sleepy". On cruise days, the waterfront buildings all become "restaurants" and bars, each with their open-sided thatch roof huts on the beach and hammocks overlooking the lagoon where you can walk out a few hundred yards and not get over chest-deep on sandy-bottom before you hit the reef where the waves are crashing.
You can find 5 beers for $4 [or could 3 years ago], and dirt cheap massages on the beach. Food is a lot for a little, and just about every building you see will sell you something to eat. There's snorkeling for those who can; there's kayaks to rent, there's bikes to rent, there's hammocks to rent.
The only time you will be showing your ID is when you try to get back into the terminal area. That is controlled-access, and it's controlled by the Mexican military -- I believe it was their navy. Except for the drug smugglers that the military keeps away, everyone is friendly and will do anything for you for a buck.
Desperately seeking 10th cruise for the free laundry.