Either in a comprehensive sense or in an interesting niche (railroad, gold mining, clothing, etc) sense. American Indian museums as well, though my personal interest is more focused on the 19th century than earlier eras. Small, out of the way museums along these lines are also of interest!
Eiteljorg Museum of American Indians and Western Art in Indianapolis.
There is a great smaller museum in the town of Pinedale, Wyoming, dedicated to the mountain men of the 1800's. Excellent displays of artifacts and storyline of the trappers that held rendezvous in the area around Pinedale. There is still a yearly mountain man festival held there each summer.
The Buffalo Bill Cody Firearm museum in Cody, Wyoming is absolutely fantastic. It has a large collection of firearms from the earliest black powders to modern firearms, a quite the collection of "old west" firearms as well. There are 6 other fantastic museums in the Buffalo Bill Cody museum center as well that are worth the visit.