I've had the most enjoyment hunting the Mearns near the Mexico border. Beautiful birds and country, and they hold for the dog. The Gambels I refer to a devils quail as they flush out so far ahead or you and the dog. Avoid desert areas with cholla cactus if you have a dog.
There are some Dusky/blue grouse in the White Mountains in eastern AZ, and also on the North Kaibab. I have only hunted those on the N Kaibab.
Like Azshooter, I have a GWP, but I think a GSP or English Pointer would be a good choice too with their shorter coats more suited for the heat and cockle-burrs. A couple of friends hunted with Brittanies too.