In Tucson? The are two outdoor ranges I can think of right off the top of my head, the Pima County one by the fairgrounds, and Mountain Park out by the Desert Museum on Kinney Road. There are two indoor ranges IIRC, both owned by The Marksman last time I went through there, one on Flowing Wells and Prince and the other on 29th between Craycroft and Swan.
If you want to travel a little bit, just past Three Points on I-19 is the Tucson Rifle Club, which has public ranges and club only ranges, which include southern AZ's only 1000 yard line. That range is a mile wide, BTW - I worked there MANY years ago.
Further north in the Casa Grande area is an outstanding free public range, unmonitored and city maintained, but it's a ways north of Tucson.
For desert/wildcat ranges refer to Title 13, Criminal Code, and last time I checked shooting was legal over one mile of occupied structures. Drive out in the desert,(public land, BLM, National Forest, NOT national monuments - those are verboten), find a nice small hill as a backstop, check for other people in the area, (no parties going on, perhaps on the other side of the hill!), that type of thing, and see how that setup works. I haven't been out shooting at a wildcat range for years, decided I like regular ranges myself. Last time I did that was Powerline Road off Tangerine in Marana, but they closed that to casual shooting due to slob shooters trashing the place.