The nearest established range open to the public is the Rio Salado Sportsmens' Club Range, at Usery Pass in far east Mesa --- follow Ellsworth Rd. north from the US 60 interchange --- it's under the huge hillside "Phoenix" sign. There is a military range just north of Florence a few miles on Hwy 79, but it is not open to civilians (and, mind the "hot range" red flags flying when artillery practice is in session!) Much of the surrounding area is off-limits to "plinking" as it is in some city's limits even though it may still be apparently rural in character, is State Trust Land open to hunting but not casual recreational use, including plinking, Gila River Indian Reservation (don't get caught trespassing on any reservation --- the tribes have been known to impound guns, vehicles, etc. --- just not worth the potential risk...) If you take the road leading east off Hwy 79 just north of the Gila River bridge, it eventually enters the southern reaches of Tonto National Forest, where it is still legal to plink. Shooters who trashed the forest with shot up appliances and computers and other junk have led the Forest Service to close to shooting an ever-growing fairy ring of Forest Lands around metro Phoenix, and the State Land Department is cracking down on the same illegal and boorish behavior in northeast Pinal County as well. South of Florence you can find places where it's at least safe to shoot in areas where you're unlikely to be bothered, even if it's not technically legal to shoot --- try the Ninety Six Ranch road, for example.
The nearest indoor range is Caswells in Mesa.