Not much shore fishing opportunities in Cancun itself. If you have a rental car, the best DIY option would be to drive south about 90 minutes, past Tulum, until you come to a bridge at Boca Paila. That time of year, there is good fishing for juvenile Tarpon (10 to 30lbs), Bonefish, Snook and the occasional Permit. Fish both on the lagoon and the flats on the beach side. Keep an eye out for the croc's when wading....I've seen them up to 12 ft long.
If you want a great day out, get in touch with Miguel Encalada at Fin Chasers..him and his son are great people and guides. They fish Isla Blanca which is about 45 minutes north of the Cancun hotel zone. They will pick you up in the morning at your hotel for a day of fishing in a panga (small outbord skiff). In January, it will be mostly juvie Tarpon and Snook. I've been out with them 3 different times, and it's always been a great fish filled day. Even small Tarpon are a blast...think of a 20lb Smallmouth...the acrobatics are insane..The Snook are like a Largemouth on speed. I like a fly rod, but spinning tackle is fun too..The fishing is in the channels and cuts of the mangroves...the water is never more than 6 ft deep and it's always dead calm.
Feel free to message me for more details on any of the above.
https://finchasersmx.com