Oo, have to disagree with The Place, at least for the Flagstaff location. It's delicious and priced well too, portions are always generous.
Little Thai Kitchen in Flag has the best Thai food I've ever had. As the name of the restaurant suggests, the place is tiny. Prices are pretty good too. If you're ordering food and like your food spicy, they have the rating system 1-5, or you could just ask for Little Thai Hot.
Bigfoot BBQ in downtown Flag below Blackhound Galleries has some delicious BBQ that's reasonably priced as well. I believe this place gets a lot of awards for best BBQ in Flag.
Thai Rama (19th Ave and Camelback & Rural and University [?]) has delicious Thai Food as well.
I'm in agreement with Chino Bandido, Thee Pitts, and Ah-So (especially the location west of 59th Ave & Bell).