There's always Ben Avery ,...
I'm up in the N. foothills so I don't make it over to the west valley often . You could always contact the BLM & ask them for areas near you open to shooting for the public. Be advised that at times here in AZ there may be no shooting due to fire restrictions imposed by State and or Federal authorities.
If possible ask for GPS coordinates, this should keep you from straying onto forbidden or private property by accident.
I know on the East side Tonto National forest has some areas and in the north Table Mesa & Black Canyon (may be) open to shooting.
Arizona gun owners.com has some places listed that only established members can see across the state.
They do this to keep every **** & their cousin from simply trashing the few ranges left free to use from being shutdown, like others in the past. If you do find one, please haul out all your trash.
For some reason people think its OK to shoot old TV's, washer machines, refrigerators, etc .. to Swiss cheese then leave the mess behind ....