Three main options for Tucson area:
SERP
Clean range, but limited options. One firing line, has a 50 yard berm on half and a 200 yard berm on the other half. They do mandatory cold ranges every 15 minutes. Lots of RO coverage. Take that as you will, but I dislike this range for anything but doing a quick zero.
Pima Pistol Club
Up in Catalina, so probably a 45-60 minute drive from DM. Lots of range options for members. They have a 100 yard rifle range and a 25 yard pistol range for guests. They also have the pit, a 50 yard handgun range, as well as 4 (?) action ranges (rifle and pistol) that can be used by members. There is a also a 200 yard range that is open sometimes, but it blocks the road to the lower action ranges. On the plus side, they have the action ranges that can be used by members- ROs don't bother you down there and you don't have to use a firing line. The negative side being those ranges are often taken already by Fudd members who want a private range, or by matches or classes that have them reserved.
Tucson Rifle Club
As you said, a long drive. They have really great amenities for rifle shooters though. There is a 1000 yard range, though I'm not sure its always open. It has pull targets like old military ranges. There is a 500m steel target range that has NRA steel targets from 200-500m. You can also drive down range to place paper at these ranges. There are several regular ranges between these two for handgun and rifle. There is some freedom to take an unoccupied range and run it yourself, if the Border Patrol isn't using for quals. I've never seen an RO on the range here.
ETA: I forgot to mention that there is a range on DM. I don't know the rules for shooting there; I shot skeet at the shotgun range there years ago. There is a rifle range out there as well that may be open to service members in an unofficial capacity.
I hope this helps. For what you're looking for I'd say TRC is your best option. The drive sucks but the range is worth it. There's also lots and lots of desert around town to shoot in, some spots are only a 20-30 minute drive from DM.