Long overdue review as this has been a favorite here, and in Tucson, for many years. For edification, "authentic" Mexican cuisine can be a nebulous and misleading generalization. There are many different regional varieties from northern, central and southern Mexico. Most of the Mexican restaurants in AZ are of the northern ilk.
La Parrila Suiza is Mexico City cuisine and excellent at that. Nice place to bring the family or dine at the ample bar if solo.
Several different combos to choose from; favorite is Parillada Mixta No. 39. Mixed grill of charbroiled beef strips two quesadillas and a bell pepper stuffed with cheese accompanied by chorizo and grilled green onions, all served on an individual little grill with mesquite charcoal underneath. Served with terrific soft corn tortillas; make your own tacos with a spoonful of cheese, chorizo and beef strips--killer!!
I eat the whole thing, but two could easily share this. Don't miss it!