Here are a list of restaurants I visit often in Los Angeles that I've found can accommodate my dietary needs when I'm on the go and have no time to cook, or just don't feel like it.
In-N-Out - Protein Style Double Double with raw onion and yellow chiles. Ask for spread on the side (the spatula they use touches bread). Fries are only thing cooked in oil.
Chipotle - Only items that have gluten are their flour tortillas. Ask them to change their gloves since they handle the tortillas. Some say that the ladles from their rice and beans could be contaminated from filling the flour tortillas, but I've never had a problem. You can ask them to prepare yours from items in the back if you are worried about this. I get their carnitas burrito bowl with fajita veggies, hot salsa, chips and guacamole. Oh and my drink of choice, an Arnold Palmer
Panera Bread - I get salads here all the time. Their website gives detailed allergen information. Again, ask the manager to inform the kitchen of your dietary needs.
Bottega Louie - Located in downtown Los Angeles, they have the most amazing bakery and desserts. They have gluten free Macaron cookies and a few other desserts. I'm trying to find out more information about cross-contamination from their main pastry chef, but I've never had a problem. The head chef's sister has Celiac, so he was more than helpful to point out the safe items for me and told me to contact him if I ever wanted to come in for a meal.
Kind Creme - Vegan and Gluten Free ice cream and cookies etc. Almost everything is gluten free.