Taqueria El Ranchito in Logan Square on Milwaukee is, despite the name, more of a restaurant than a lunch counter, with a full bar, and they definitely know how to make a burrito (and are pretty good across the board whatever you want). However, while completely fine and very typical of its kind, El Ranchito might not be conducive to the type of family-visitation meal you are looking for and/or meet your mom's expectations on ambience, because it's sort of a standard, semi-claustrophobic and dimly-lighted fonda/cantina sort of atmosphere. I mention it, however, because I think it's a notch better than El Cid II, mentioned above (which I think would be a good choice, but actually does a better job on Cuban food than Mexican at that location) and my next recommendation, La Puebla (below), which is prettier to visit but not as delicious.
La Puebla would likely be an easier sell on the aesthetics, if slightly less delicious on the food. They definitely have you covered on burritos, and they also do gringo-killer frozen margaritas, etc. The decor is 1987 festival marketplace Mexican restaurant preserved in amber (and always impeccably clean, well-lit, breezy, etc. ... certainly "nice ambience ... good for mom").
Finally, you might want to consider
Las Asadas on Pulaski just north of Belmont. I've never been, although I believe gleam had some good things to say about their carne asade, which I assume would translate well into a nice carne asada burrito. It's located in a former Pepe's restaurant location (full-service, sit-down restaurant) with its own parking lot.
Taqueria El Ranchito2829 N Milwaukee
Chicago, IL 60618
Phone: (773) 227-1688
La Puebla2658 N Milwaukee Ave
Chicago, IL 60647
(773) 227-5499
Las Asadas3243 N. Pulaski Rd.
Chicago, IL
(773) 283-8832
Edited to note that Semper Fudge also highlighted Las Asadas, above.
Last edited by
JimInLoganSquare on October 14th, 2012, 8:16 pm, edited 1 time in total.
JiLS