Overally, Christi's Restaurant List is probably your best bet as a jumping-off point.
My own short-list includes:
El Pique for tacos
Los Chilangos for huaraches
Los 3 Gatitos for panuchos and salbutes
Los Otates for posole and tacos
La Candela for home-style meals and nice Tikin Xic (fish in banana leaves and achiote)
Parilla Mission for breakfast, home-style meals, tortas, and arrachera (open breakfast to supper)
Camilo's for shrimp and fish tacos
El Capi Navegante for seafood (my kid loves their octopus ceviche)
La Choza for breakfast (this is another all-day place but doesn't float my boat apart from breakfast. Many people adore it, but I think La Candela is better.)
Kinta for fancy, creative Mexican dinners
El Super Hit has tortas de cochinita that are nice to take for lunch on the plane home
Note that some of these places are lunch-only, most dinner-only.
There are many more, and everyone has their favorites. I love me some fancy food, but in San Miguel de Cozumel we always seem to end up going more mid-range or quick, cheap eats and loving every bite.
"Authentic Mexican" covers an awful lot of territory, so if there's something in particular you're looking for it might help to specify that.
Thanks mstevens!
I'll add Kondessa to the list now too!
It is a new place, by the same owner as Kinta - but more of a traditional Mexican menu - burritos, enchiladas, tacos, fajitas, etc. DELICIOUS with great service and atmosphere!
They are located on Av. 5 between Calle 5 and Calle 7 Sur on the right hand side of the street (it's one way).