Tempe and Mesa used to be my home away from home for a while, but have not been in maybe 7 or 8 years. Sorry if this is too outdated, but here goes.
I have not been to Papago Brewing in a long time, but it was a favorite. It was mainly a beer bar with a good selection of West Coast beers, and a few of their own labels contract brewed at another place. It is a little north of the airport area on rural/Scottsdale Rd and McDowell.
Four Peaks was also a favorite. Near ASU.
You should be able to find many beers we don't get in MI at any bottle shop. Sun Devil liquor was one place I used to stop sometimes.