Hi sewenfly I did a bit of flyfishing in the lagoons with a tour guide flyfishing tours a think it was the fishig was amazing catching barracudas these are some fish to catch but if your of the beach I suppose you could catch red snappers etc there also hard fighters I was told good luck!!
We stayed in an all inclusive resort on Rivera Maya a few years ago, near Playa Del Carmen. I caught bonefish on the fly before breakfast most mornings. There were also a couple of milkfish and some others I could not identify. I was fishing blind, rather than conventional sight fishing, wading out as deep as I dared, then casting back towards the beach and into likely looking areas. Nothing huge, average about a pound but even a half pound bonefish puts up a good scrap. Especially when a big barracuda decides it wants it for breakfast! That was scary. This thing came flying past me and grabbed the bonefish right in front of me.
The problem is most of the beaches are part of individual resorts and security will move you on. I fished early in the morning to avoid the security guards. If you can find somewhere quieter I am sure you could do ok.