Good Mexican near LAX
I haven't been in ages but LAX Tacos on Arbor Vitae in Inglewood used to be a regular stop when I worked around south of LAX. It was always busy with mostly locals, obvious LAX employees (LAX badges, uniforms, etc.) as well as "Our City's Finest" from LA and Inglewood. I don't recall if they have what you are looking for, but I do remember their taqueria food was pretty good.
543 W Arbor Vitae St, Inglewood, CA 90301
My wife loves the lengua tacos from LAX Tacos, and I used to be partial to the carnitas tacos. However these can be hit 'r miss depending on how fresh (and moist) the carnitas are. Best bet - get 2 chicken tacos and 2 carnitas tacos - you can't go wrong with chicken. No mole here, but they do have OK menudo on weekends.
If you are in Westchester LAX area, I'd recommend Taqueria Sanchez over on Centinela (@ Culver blvd.). Great shrimp burritos and pretty much "budget." Get 2. They come wrapped in foil and I've actually refridgerated one and heated it up next morning for breakfast. Carne asada and al pastor tacos are ok here, but shrimp is the way to go.
I really like TS and the Centinela location is easier for me than the Inglewood Ave location But from Century Blvd to the Centinela TS is about 20 minutes from the time you get in the car to the time you get out. The traffic on both Lincoln and Sepulveda stinks on a good day... But still a great rec for the poster if time allows...
PS: I have noticed a staff change in the kitchen at Centinela TS over the past few months, and IMHO, it's slipped a bit. They've gotten my to-go orders wrong a couple of times (at my expense), and I've noticed that the place is losing its edge in general. I may have to return to the original location to compare...
Personally, if you're down in that area, for tacos I prefer Don Felix (corner of Washington & Sawtelle, down the street from Titos) over TS. Just my preference. Have not tried other items on their fairly large menu (tortas, burritos, etc). But, don't think it quite matches your criteria, except for being light on the wallet.
For chilaquiles, also in the MarVista area, is Pepe's Galley (in Mar Vista bowl on Venice near Centinela). Had parmesan cheese topping (I believe) and seemed more about the quantity than quality, but worth a try as it's well-known to chilaquile hounds. Definitely more "blue coller" compared to Mi Casita's (in Bell) more refined chilaquiles.
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For chilaquiles I recommend Lichas in Hawthorne. For the others I'd search for the recent topics on 'Lennoxico'.
Click through to List, then to Place, then to linked Topics.
http://www.chow.com/lists/54 - Hawthorne
http://www.chow.com/lists/87 - El Segundo/LAX
http://www.chow.com/lists/89 - Inglewood/Lennox
I'm in Westchester, too, and our favorite Mexican restaurant is Paco's on Centinela, just south of Washington. I'm partial to the tamales, and their tortillas (both corn and flour) are handmade. Prices are pretty typical for sit-down Mexican. It's very popular, so you may have to wait if you go at regular dinner time.
They have another location on Manchester, west of La Tijera, but it just doesn't seem to be as good, IMHO. The hand made tortillas are one of the biggest draws for me, and the Manchester location seems to use the typical mass produced kind.
My SO just pointed out that Paco's doesn't have chilaquiles or mole, but I think it's still worth a visit for typical SoCal Mexican food.