Marksman Pistol Institute ran both indoor ranges, one on 29th, and another on Flowing Wells and Prince when I lived there, and I worked at the Prince range when it was owned by Jensens. Also a public range tucked away in Tucson Mountain Park, rather nice place. I worked at Tucson Rifle Club out past Three Points, an awesome place - the range is a full mile across, 7 different outdoor ranges, including the 1000 yard range. BUT, you must be a member to use the ones other than the 100 yard public and 500 meter silouhette ranges.
Murphys is nice, West o The Pecos used to be a good little gun shop, but it's been a while.
AZ has Consitutional Carry, but if you want to avoid the Brady background phone call, (takes 5 minutes), and would like to carry while NOT drinking in a resteraunt that serves alcohol and isn't posted, (Olive Garden comes to mind), get your AZ permit, very easy to do. No magazine limits, amo restriction, NFA friendly, no AWB, actually, not many restrictions at all firearm wise, and getting better every year.
C'mon down - I lived in Tucson for 40 years, BTW, since I was hatched.