Pre-theater casual dinner spot?
There is really very little within walking distance of the Music Center, maybe Mendocino Farms, which is casual but not divey. There are places within a short drive with free parking. Depending on which night you're going, The Park's Finest, less than a mile down Temple with street parking, has great Filipino style BBQ. Phillippes, as mentioned, has free parking as well.
It is always difficult to know what someone considers "walking distance." The area directly around the Music Center is very limited in terms of food options. In the Music Center itself is a little kiosk with an attached taco stand, but the tacos are just okay and expensive compared to what you would get elsewhere.
Border Grill is casual and its bar menu is pretty inexpensive. It is at the corner of 5th and Figueroa, so it isn't that far. In the daylight, walking to the Ahmanson should be fine, but I would be a little concerned about wakling back at night (if you park by the restaurant) because some of the area is sketchy. Border Grill does have a free shuttle service to the theater, so you pay for parking ($5 with restaurant validation).
If you want awesome Mexican food, go to Mexicali Taco & Co., a real hole-in-the-wall on Figueroa north of the 101, for tacos, vampiros and cachetadas. But Mexicali is about .5 miles away and you probably wouldn't want to walk. However, there is free parking in the tiny lot and usually street parking available, so you could go to Mexicali, eat, an then drive to the Music Center and park. http://mexicalitaco.com/
Just across the freeway in Chinatown is Phillippes, home of the original french dip. I love the lamb dip. Very casual and complete with sawdust on the floor. An LA landmark. Plus free parking too.
You can always walk down or take Angeles Flight down to Grand Central Market and all their food stalls. They do close at 6pm.
There is a Pitfire Pizza close by on 2nd Street
Farther away is Umanicatessen on Broadway.
The Nickel Dinner
And Wurstkuche for wonderful sausages.