I lived in Phoenix for 16 years and saw the scene grow into a livable vegan city! Some great options are Green and Nami, owned by the same great guy, in Tempe and Phoenix. Copper Star Coffee in Phoenix makes great coffee and has rad vegan baked goods daily. They also have a few non-dairy milk options and some cute baristas. Aside of Heart in downtown (formerly Conspire) has raw vegan food and great punk shows out back. There are more expensive vegan restaurants (True Foods Kitchen, Fresh Mint, Pomegranate Cafe) but Green, Nami, and Copper Star are all you need for every meal of the day and some after-dinner drinks as well.
I love Arizona and I know it can be hard to imagine that it's a great place for vegans, but there are multiple farmers markets, the new Whole Foods on Camelback has an in-store bar and a giant selection of vegan options in the hot bar, and the Phoenix Anarchist Coalition has get-togethers that always have vegan chili to share. If you have any questions about being vegan in Phoenix, ask me! I currently live in Portland, Oregon so I have some information about being vegan here too.