do you think it would be possible to find a room at Butte/Boise without prior reservation at the middle of Aug?
I don't think you would have any problem, as long as you are not locked into one particular hotel chain. They are both decent size cities on Interstate highways and there will be a good selection of hotels near the main interchanges.

In Butte, I see 10 hotels listed on hotels.com, and about 40 in Boise.