Drive south for about 2 hours from there for the best opportunities - bones, snook tarpon, permit.
I believe most of the water to the south of Cancun, including around Playa Del Carmen and continuing past there through the Akumal area all the way to Tulum is a "reserve area" and is off limits to most sport fishing. There's some areas directly to the north of Cancun, as well as in the bay adjacent to the hotel zone that's open, but you would do best with some type of watercraft. Best to check the local reg's. Also, you can take the ferry to Cozumel from Playa and hire a guide for the day to fish the flats out there.
Your best bet is to go south past Tulum and beyond to the end of the "road". Lots of flats down there, but a guide would be a worthwhile investment there as well, although some DIY may be feasible.
Watch for salt water croc's, stay safe, have fun and bring back pictures.
I'm in Cancun January 21-30. In the past when I've been down there I've spent a couple days at Pesca Maya on Punta Allen in the Ascention Bay area-lots and lots of bonefish! I've also fished with Cancunflyfishing.net. They pick you up at your hotel and I fished north of Cancun at Isla Blanca. Not too many bonefish in the winter but hooked some baby tarpon and some snook. This time I'm taking my two son-in-laws to Cancun Lagoons with Cancunfishing.com. It is very close to the condo we are staying in and they have a boat that accommodates 3 fishers. Nice place to be in January! Have fun, Rick