I will always love La Choza, where I had my first meal on the island. At times it's completely filled with tourists. At others, it's completely filled with locals. I don't care how touristy it may have become, it's good food, good staff, and clearly popular with locals. The comida del día is always great. It's where we take anyone who has any trepidation about getting killed to death by dangerous Mexican food until they die from it, because once they enter you can watch them visibly relax, and by the time we leave they're always going on about returning.
I really don't get the whole "touristy" thing, like it somehow makes the food not as good if "tourists" go there. Guess what; aside from those of us who have moved there we are all tourists. Of course, it can be taken to the extreme; I have never been in Margaritaville or Señor Frog's and don't plan to, ever.
But, anyway, La Choza has always been on my short list of eateries to visit when I am on Cozumel. I liked the old location a little better, but their food has always been excellent. Fish in mustard sauce, mmmmmmm...