I would certainly encourage the locals to visit the park during autumn, as this is a beautiful time of year, particularly along Grasshopper Creek, which was the gold-bearing creek that attracted all the miners so many years ago
(Click on photos to open large size view.)
Grasshopper Creek still flows around the edge of town. There is a nice little campground alongside the creek, just west of the town itself. It is within walking distance. I've never caught a fish there, but that didn't really matter.
One other benefit of a late autumn visit is that there are NO bugs. None!
These photos, of the town, and of Grasshopper Creek, are from the Bannack State Park Homepage. Be sure to visit.