Thanks to Go Dairy Free viewer Lori for emailing this recommendation:
I wanted to recommend Flame Broiler restaurant, it is completely dairy free! We eat there regularly and love it. I think it is mainly based in California.
Touted as a healthy Asian-style rice bowl restaurant, this chain is not only dairy-free, but also free of MSG, high fructose corn syrup and trans fats (according to their website).
At this time, they have a heavy concentration of restaurants in California, but also have locations in Arizona, Florida, and Oklahoma. They appear to be expanding quickly. See their website for current and upcoming spots.