I certainly don't have all the answers, but I hope I can help point you in the right direction. There are many out there much more experienced and well-versed than I, since I live in the U.S., but I've been to this area many times and will try to help.
FYI- As you've probably already noticed, it's very tough getting information on this type of fishing in MX along the "Riviera Maya", as that area of the Yucatan is called. Most Mexicans don't even think about fishing inshore as really fishing. Their mindset is geared more toward offshore species, like marlin and sailfish and dolphin (dorado). Inshore fish are more like trash fish to most.
You CAN fish from shore and catch fish, despite what most Mexicans will tell you. Why? HELLO! THEY WANT TO SELL YOU BOAT TRIPS! That aside, there are some basic strategies that hold true for the Mexican Caribbean/Mayan Riviera.
The area you've mentioned is ripe for shorefishing (Cancun to Coba). If you're staying in Puerto Morelos, you'll be staying in what used to be a small, sleepy fishing village just south of Cancun that somehow got hopped over in the massive buildup of hotels and resorts down the coast. It's beautiful, and the northern part (closest to Cancun) may be the most beautiful and pristine and prime for fishing. As for the shore fishing, well, you'll have to check it out for yourself. Never tried it there.
If you are using spinning tackle and enjoy fishing with artificial bait, bring some rubber tailed jigs and various lead heads in different weights. I've found chartreuse, root beer, and lime green tails with white and red heads work pretty good. In addition, bring something like mirrolures, top water zara spooks, or bomber plugs. These can work very well casting from shore into the surf at night. I have caught several snook this way with my good Mexican friend Enrique Soto Tapia in the Cancun area, who also has a ponga to do ocean charters for dorado and such. (Gracias, Enrique amigo).
Don't be afraid to wade fish along the coastline. It's very similar to fishing along the Florida coast this way. As always, be aware of your environment.
If you are a fly-fisherman (which I am not), look for posts from Hank from Canada. He is well versed and graciously generous with information about fly-fishing Maya Riviera.
You can also fish live bait. HELLO! Yes, the fish like that! You can even get them the old fashioned way. Get some cut shrimp, squid, oysters, etc. and use a small hook to catch the live "shiners" (many different species). If you're really adventurous, you can bring a small bait net in your luggage. Now, we're talkin'! Flip these out in the surf and kick back and relax.
Sunrise and sunset, or after dark, seem to be the best fishing overall.
Here are some species I have caught from shore or wading:
2. yellow tail snapper
3. cubera snapper
5. mangrove snapper
6. crevalle jack
I hope this has helped you and you catch a LOT of fish and enjoy your trip!
Thank you SO MUCH for your help! It has been impossible finding info anywhere else on the net, much less such specific details like you gave... thanks a ton!
You're welcome, CallieB. Best of luck and enjoy.