http://www.phoenixrodandgun.org/ A club with a range in south phoenix
http://www.rsscaz.com/ A club with a range in east Mesa
https://www.azgfd.com/shooting/basf/ A range with clubs in north phoenix.
all 3 have public ranges and competition ranges and active competition groups
Both RSSC & PRGC are true member-run clubs, both lease their dirt (RSSC from AZGFD, PRGC from PHX city park). both have public ranges and hours and members-only ranges and hours (much more enjoyable)
Ben Avery is a AZGFD owned and run facility, landless clubs reserve the various ranges and run shoots there.
A smaller range, Joe Foss range in Buckeye, an hour west of Phoenix, is run by ASRPA. http://www.asrpa.com/
or wait till it rains and they open up desert shooting
Tonto NF is North and east and has a huge swath of closed-to-shooting areas closer in to town, see the USNF web pages for maps & rules.
BLM is mostly west
Yavapai, Coconino, Kaibab, Apache-Sitgreaves are the NF way up north
no target shooting on State Trust Land, but hunting is OK.
Shoot good
Poole
http://arizona-rifleshooting.com/