Have you been to Old Tucson not far south of Tucson? I was there during my freshman year in college. It was built as a movie set in 1940. I heard they had a devastating fire several years ago, so check before going.
I believe Bannock, Montana, was taken over by the state and is now entirely a state park. I saw photographs of Bannock that were taken during the 1930s, and a number of families who had been displaced because of the Depression were living in the abandonned buildings. During the 1930s, a number of very small Western towns had an upsurge in population because people who had been displaced elsewhere moved to them simply to have a roof over their heads. Looking for living history? I would suggest going to Columbia and Bodie in California.