In North Carolina: CookOut - they have 30-some flavors of amazing milkshakes (including eggnog shakes in December and watermelon shakes in July!), and great cheap burgers.
In New Mexico: I echo
ButIsItArt on Dion's. Also, I grew up on
Blake's Lotaburger - amazing green chile cheeseburgers and fries, and they write your order directly on the bag they put it in, so it's guaranteed to be accurate.