The produce in American grocery stores looks perfect but has no discernible taste, The produce in Mexican markets has gouges, bruises and imperfections, but tastes wonderful.
Priorities.
The place is vibrant with life that you don't get in any American-style grocery. It's a feast for the senses.
Don't expect fast or snappy service at the lunch counter. There's usually a line. Knowing Spanish helps a bit, but there's usually someone around who can translate. For your patience you will be rewarded with the real tastes of Mexico: The gristle of lengua, the insanely savory flavor of the carnitas, the wonderful aroma of the barbacoa.
Just go. Pick up some real tortillas and some Coke in real glass bottles too. It's still made with sugar, dontchaknow?