I'm a vegetarian, and a pretty strict one, so I never trust any chips, beans, rice, soup or masa based dishes at Mexican restaurants. I have even stopped asking if they use lard or cook in chicken stock because I always either get the feeling that the servers (1) don't understand what I'm asking about (this has mostly happened with servers for whom English is a second language) (2) tell me what they think I want to hear.
With that said, I did have a really delicious vegetarian dish at Tepatulco a few weeks ago. It was pasta with a chipotle sauce and little patty-pan squash and mushrooms. That is not a cheap restaurant, though.
There are only two true vegetarian friendly Mexican places I can think of right now, other than Frontera, Topolobampo and those other higher-end establishments.
One is Mamacita's on Clark, north of Fullerton. This is kind of a dive and it tends toward the more toward the Fresh-Mex kind of Mexican food, but it's not bad and it's dirt cheap. It's also BYO which is nice.
The other is Adobo Grill. Again, probably not the most authentic Mexican, but several veggie options are available and it's not too expensive. They have two locations, one in Old Town and one in Wicker Park.
Mamacita's
2439 N Clark
www.mamacitarestaurant.com
Adobo Grill
1610 N. Wells
2005 W. Division
www.adobogrill.com