If you happen to be going into NE New Mexico,, there is the NRA Whittington Center in Raton. Their museum, and ranges are worth the visit.
But I found that a little town about 30 miles away from there very fascinating. In Cimarron, NM. there are a couple of places that have a lot of old west REAL history.
The St. James Hotel,, a MUST visit if there,, where there are still bullet holes in the ceiling, and several famous & some infamous types stays, had killings etc. The history of the place is outstanding.
And also in Cimarron is the Old Mill Museum. Again,, lots of old west history that isn't "Hollyweird" crap.