If it's the Groundlings thing on Highland to which you refer, Chowpatty's list is good. Fwiw, I have tried to walk into Mozza on four separate occasions, including twice at 3 or 3:30 p.m. on a weekday, and have always left hungry after being told the wait was 45 minutes to an hour for a seat at the counter.
In addition to CP's suggestions:
Angeli Caffe (http://www.angelicaffe.com/menu.html ) is within walking distance, and they have pretty good Italian/pizza, etc.
Ammo (1155 N. Highland Ave., (323) 871-2666), which is a bit more expensive and a bit fancier (serving French Cal fusion with a healthy spin, I guess) is also within walking distance. I love (!) their chicken and veggies on brown rice, and I don't usually go for the macro-neurotic stuff.
East India Grill (345 N. La Brea Ave., (323) 936-8844) is close enough to walk and has (I think) very nice Indian dishes. I am totally addicted to their eggplant bharta, chicken tikka, and their lamb korma. Good nan too.
Also, you could walk down and brave the line at Pinks (a local, sort of famous hot dog stand) which is at the corner of Melrose and La Brea. I personally don't think it's a transformative culinary experience, but it's fun and it's very LA.
At the extreme opposite end of the spectrum, Providence (http://www.providenceLA.com ) is within walking distance and has some of the best seafood, and perhaps even food generally, in the city. Providence won our 2006 LA Chowhound poll (http://www.chowhound.com/topics/357211 ), but it almost certainly fails your requirement that the place be "casual." (And it's definitely not inexpensive.)
Lastly, when you get done with the Groundlings, and if it's not too cold, you might want to drive up La Brea for some ice cream at Mashti Malone's (1525 N La Brea Ave., (323) 874-6168). Excellent ice cream with lots of interesting Persian flavors alongside more traditional choices. Uniquely LA, I think. (Their black cherry is superb.)
Hope you enjoy your visit!
Red Pearl Kitchen on Melrose if he likes Chinese/Asianish food, very stylish.
The Pig on La Brea near Melrose for very casual but decent barbecue.
Mozza, the much-discussed new pizza place at Melrose and Highland, if you can go early and/or sit at the counter.
Luna Park on La Brea just north of Wilshire for well-priced food in a fun atmosphere with good drinks for you.
Cube, on La Brea near Melrose, for pasta, sandwiches, pizzas and excellent cheese and charcuterie.
I think the only decent sit-down place that's walking distance from the Groundlings is Azami Sushi, if he likes sushi.
I'm not sure whether the Village Idiot, the new gastropub place on Melrose, is only for over-21s or not.
That should give you a start!