Been a few years since I lived out there (91-95) but there was a shooting range just off the old Hiway 89 between Layton and Kaysville. Think it was called Davis County Shooters or something like that. It is all outdoors, but they had short and long distance ranges available. It's not too far south of the Valley View golf course. Maybe one of the locals can confirm if it still exists.
I also thought that Hill AFB had a place to shoot, though I never actually shot there if they did.