Tour the World Museum of Mining (<-- website linked)
Suggested time frame - 1 hour for town area and indoor museum, 2+ hours for underground mine tour, town, and indoor museum
Suggested age range - 5 and up for town and above ground museum, older kids and up for underground mine tour (5+ are permitted, but the guide does a lot of explaining and it's a little musty/dark underground so young kids may not like it)
Cost - 4 years old and under: Free
5 and up: See website
Additional notes - Very knowledgeable staff and a really unique place. Getting to head a hundred feet underground and see the real conditions in which miners work was an eye-opening experience. Just be mindful that you need to book the underground tour online ahead of time and maybe a few days in advance.
Visit the Granite Mountain Speculator Mine (<-- website linked)
Suggested time frame - 15 to 30 minutes
Suggested age range - Middle school and up
Cost - Free
Additional notes - This is a beautiful location to see expansive views of Butte and learn a little more about its history. There is a lot of reading involved so older kids would best benefit.