My favorite place, Mi Tierra," also has music. The food is the best:
http://www.mitierrarestaurant.com/
Lalo's is my second choice. It has a few restaurants with the first (1971) in its original storefront in Little Village. Now there are 11 more locations. See below...watch the intro:
http://www.lalos.com/
La Condesa 3 is a gem that looks like it was a truck stop about 20 years ago. Today it has a truly authentic menu:
http://www.urbanspoon.com/r/2/13911/restaurant/Pilsen/La-Condesa-Restaurant-3-Chicago
Nuevo Leon is very popular with many hungry Mexicans but not my favorite. It's located on 18th ST:
http://www.nuevoleonrestaurant.com/
For upscale Mexican gourmet, try the New Rebozo in Oak Park:
http://www.yelp.com/biz/new-rebozo-mexican-restaurant-oak-park
Another Oak Park upscale Mexican restaurant is Fuego Loco. It has another location in Elmhurst:
http://www.fuegoloco.com/