Well, sorry for one of you that my post is post-Mem Day weekend, but man, there have been some great suggestions here. Phillippe's is a must not just for the food but for the setting/atmosphere as well...so un-"LA". Make sure you check out LA's Union Station 2 blocks down across the street...one of the truly great train stations in the country, and even better now that it is being used much more lately! Langer's is another great one...I can only imagine what would be said if it were in NY. And Cassell's is one that I have never been to but I hear real good about it...one of these days..sigh.
That being said, I'll toss out a few more. I just don't know how your time/geography lay out, SoCal is big, and the chowishness (or is it LTH-ness?) extends far and wide. Most of my suggestions are just south of "LA" in Orange County.
1. Steak Dinner at Trabuco Oaks in Trabuco Canyon (Orange Cty). DOn't wear a tie here...it's rustic casual, but the steaks are first class without the stratospheric prices. The last dinner I have in SoCal will be here...a filet with their mountain of first-class shoestring fries sitting in a dark room with a tree growing through the the roof.
2. Babyback ribs and Tulsa Potatoes at Tulsa Rib Company in Orange. Well if dinner is above, then lunch is here. BBQ purists be damned, this is these are the best ribs I have ever had, and that includes Chicago, Memphis, Kansas City and elsewhere.
3. Italian Sausage at Sabatino's - Newport Beach. This is related to the Sabatino's in Chicago...but the sausage is unique here. Unreal stuff. Great place for a Sunday brunch as well.
4. Ok, let's jump up north...I like a great steak, and "Santa Maria"-style BBQ is unique to CA. Lots of choices, and the meat can include tri-tip, sausage, steaks, beef ribs and more, but if I had one choice it would be dinner (meat of your choice and don't ignore the pork chops) at Jocko's in Nipomo (make sure you pay the extra for cooked over the oak). Hole in the wall place but the food is worth the drive. Other great places locally in the area include Far Western Tavern in Guadalupe and Hitching Port in Casmalia as well as the THursday ight Farmer's Market in San Luis Obispo.
5. Got to include a chain somewhere here. Rubio's for fish tacos, In-N-Out...so many others, many unique to SoCal. IMHO, the best chain here is Ruby's, a 50's-style diner/burger joint...not fast food, but a fun place with good food. Everything I have had in many visits there from breakfast to burgers to salads to milkshakes...it's all better than it probably needs to be. I equate it somewhat to Portillo's in terms of a place that can please most everyone.
Finally, if you want a "Chicago" fix, I'd welcome you to try out and critique a couple of Chicago offerings in SoCal. There is Portillo's in Buena Park, but for local flavor, italian beef/sausage at Chicago's Best in Irvine (my pick) or Taste Chicago in Burbank and Stuffed Crust pizza at Tony's Little Italy in Placentia (my pick) or Chicago Pasta House in Moreno Valley.
All the above places are family friend;y non-pretentious places that won't break the bank...and trust me, it's way too easy to do that at a lot of places in SoCal. Happy travels and dining.
Ah heck, I keep thinking of more. If you have a donut fix, the BEST donuts in SoCal that I know of, although it has been 10 years since I've been there, were the giant creations at Blinkie's Donut Emporium in Woodland Hills. And for ice cream, there's lots of great choices...my picks are Hans' in Santa Ana (near South Coast Plaza) and, heck if you're up north for #4, hit Doc Burnstein's in Arroyo Grande.
Bob in RSM, CA...yes, I know, it's a long way from Chicago