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As a preface, I would like to note that my request was for information
relating to restaurants near Sherman Oaks (in the San Fernando Valley).
Los Angeles is a big place, and no single post can effectively cover all
the ground.  Also, as I am a vegetarian, the suggestions may not cover some
other very good GF-friendly restaurants in this vicinity.

During my short stay, I dined at 3 restaurants.  All were excellent.

1)  Skirball Cafe (inside the Skirball Museum).  This is located on
Sepulveda Blvd., just south of the tunnel underneath Mulholland Drive,
and is also adjacent to the 405 (San Diego Fwy.).  I had a chop salad
(about $10).  The vinegrette dressing was the best I've ever had.  There
is a great menu with all kinds of very fresh and appetizi ng foods and I
would highly recommend it.  Plus parking is free and easy!

2)  17th Avenue Cafe on Montana.  This is in Santa Monica.  Had a homemade
vegetable soup that was very good, but might have used a bit more flavor.
Then a grilled vegetable chop salad ("chop" seems to be big in L.A.), which
was also very good.

3)  Daily Grill in Encino (on Ventura Blvd.)  They have a website at
dailygrill.com which is comprehensive and includes their entire menu in an
easily accessible format and also shows their 12 or so locations.  Had the
Grilled Vegetable Plate (Grilled Vegetables with Steamed Spinach, Broccoli,
Green Beans and Cauliflower, also available with Baked Potato).  About
$14.  Another winner.

Recommendations from listmates (thank you to those offering help!) follow:

The Cheesecake Factory just opened up in Sherman Oaks, corner of Sepulveda
and Ventura Blvd.

Tempo restaurant in Encino is nearby and has a wonderful mid Eastern
vegetarian assortment. Of course it has a lot of dips so one should
bring their own rice crackers or rice cakes because the serve with Pita
bread. There is a Trader Joe's in Sherman Oaks on Riverside and
Hazeltine also. There are several; restaurants that I eat at often in
S.O.  One is Marmalade, one is Cafe Cordiale, one is Cafe Bijou. I am
not a vegetarian so I am not as knowledgeable about that, but the all
have great salads. Stanley's in S. O. makes the best Chinese Chicken
Salad in the whole world using rice noodles. You won't have a problem
out here. The restaurants are all used to people with all kinds of
dietary requirements.

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May I suggest Valley Inn on Sherman Oaks Place in Sherman Oaks? Also, Tony
Roma for Ribs on Ventura Blvd. in Encino. Although they are not vegetarian,
Valley Inn has a pasta/vegetable entree on their menu.

KooKooRoo, a chain of casual dining restaurants offers several
vegetable "side" dishes. They have a store in Encino, as well as one in
Studio City and Canoga Park.

The Sherman Oaks area between Van Nuys Blvd. and Sepulveda Blvds. (near
Whole Foods Market) has many small restaurants which offer vegetarian,
Indian and health food menus.

Genmai Sushi is in Van Nuys which is quite near to Sherman Oaks. They
have great vegetarian good,and while not specifically gluten free, they
are knowledgeable and eager to please.

The Celiac Disease Foundation is also nearby. Look them up in the phone
book, they will have a restaurant list.

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I've found this link so far.
http://www.larestaurant.com/vegetarian_cuisine.htm

I haven't been to these places, but I thought you might be able to call
the phone numbers and ask. I know there are some really good vegetarian
restaur ants in the area, but the ones I've been too are usually heavy
on the whole wheat, semolina, tempeh, hvp, etc. And the ones that do
cater to a wheat-free diet have a fair number of oat dishes. It's
tricky. I've seen at least two that do rice noodle based soups. With my
other food allergies I haven't been able to try it out.  Native Foods is
in Westwood and has an online menu and restaurant location:
http://www.nativefoods.com/ Then there's Real Food Daily:
http://www.realfood.com/ Only saw a couple of safe things on the menu.

And Follow Your Heart Restaurant and Cafe:
http://www.followyourheart.com/index.html (21825 Sherman Way, Canoga
Park, CA 91303 (818) 348-3240) Saw a few things on their menu.

Thai restaurants serve rice noodle dishes, and Sherman Oaks has a few.

Charm Thai (13539 Ventura Blvd., just east of Woodman, Sherman Oaks
818/990-7384) does st eamed veggies, curried tofu, and a few other
things. I'm not sure about the spices and prep.

The Asian and sushi restaurants are another option. I prefer vegie
sushi. There's a sushi restaurant in Little Tokyo that'll do cooked
veggie dishes; you have to explain carefully what you can and can't
have. More and more of the restaurants in CA are diversifying the menus
in favor of vegetarians; it's just a matter of spices, sauces, etc. and
me remembering what all is up that way. Here's a list of Japanese
restaurants in the area if you'd like to try:
http://www.californiaroll.com/docs/english/categories/11/index/index.07.
html

I'd try the hole-in-the-wall places. I've found it's easier to explain
dietary restrictions that way.

Some of the larger mexican restaurant chains will do veggie fajitas.
It's normally zucchini, bell peppers, and squash. If you call ahead of
time an d explain they'll make it without seasoning. You can substitute
avocado slices for the guacamole.