If you ever make it to the east coast, Lucky’s Burgers & Brew in Roswell GA is the most dog-friendly place that I’ve ever seen.  Big outdoor, fenced-in patio with lots of families and dogs enjoying meals together, and a nice pet-free interior for people who don’t like dogs, but since the interior walls are completely covered in pictures of dogs, you’re really surrounded by them.
 
Julie Darling Donuts in Chattanooga TN also has a large pet-friendly patio.