Actually Arizona is a pretty well knows state for bird watching.
You might base your self in Yuma and just north is the Imperial National Wildlife Refuge.
But even Tucson, Phoenix, and the Lake Havasu areas have some pretty good nearby places for spotting those critters. You pretty much can't go wrong no matter where you go.
Green Valley is a beautiful area, and Apache Junction is very popular too. Both of these areas are surrounded by desert and less populated. There are a lot of hiking areas, so I would imagine the bird watching is pretty good.