I hope you will get to Santa Monica while you are there. It is great for strolling on the beachwalk, and Main St. if fun for strolling and shopping, as well as the Promenade and the farmer's market if you re there on those days. Main St. farmers market is great on Sunday mornings. And walk the entire length of the famous Santa Monica pier at dusk as sun is setting, see the famous art deco neon light sign, the ferris wheel on the pier, and of course, sunset over the ocean at end of the pier.

If you do go to Santa Monica, do NOT MISS the wonderful Mexican restaurant on Main St. called Lula Cucina Mexicana. It is WONDERFUL!!! Happy hour is great in the small and very colorful bar. The servers and bartenders are all from different places in MX, including Puebla and Oaxaca, and these folks know how to do seriously authentic and GOOD Mexican food. This is NOT TEX MEX. The bar has the best margraitas and selection of Tequila and mescal I have seen and had anywhere in the USA.

GO TO LULA

http://www.lulacocinamexicana.com/index.html

I definitely agree on Santa Monica recommendation!

L.A. has a lot of good Mexican food, needless to say a lot of them are the tiny hole-in-the-wall places. I'm sorry I don't have the name of the ones we where we have eaten with our son. Try Yelp for recommendations on some of these little, usually family-owned places. You will be in for a treat.

A hole in the wall that I like in Santa Monica is Gilbert's El Indio. It has been there forever. It is an authentic old school LA/Mex restaurant (cash only I think).

http://www.yelp.com/biz/gilberts-el-indio-restaurant-santa-monica

I haven't been to the Loteria Grill in Santa Monica but the Farmers Market one is good, if overpriced for what you get.

http://loteriagrill.com/locations/santa-monica.html

If you are in the area south of downtown - around USC - La Taquiza at 30th and S. Figueroa - is my favorite little place.

Very popular with the students and it has the best Carne Asada tacos - and the secret is he marinates the meat for 36 hours, and it's very reasonable. see: http://chowhound.chow.com/topics/335200

Here are 2 in the Santa Monica area. I've been out here 20 years and these are 2 of my favorites:

1. El Cholo - Traditional Mexican. Family owned since 1923 (Website: http://www.elcholo.com/)
2. Border Grill - Upscale Mexican (and close the the 3rd street Promenade) (See: http://bordergrill.com/)