A few of my favorite towns that have lots of history with mining are Butte, Anaconda and Virginia City. Depending on where you are they are all within a short (1-2hr) drive.
I am a big fan of the Crazy Mountains. They are best viewed by driving to Wilsall, MT. The look big because of all the hay/prarie land surrounding them.
If you are up for a drive, the prettiest road in Montana is the Beartooth Hwy between Red Lodge and Cooke City. It may be closed in October so if you do go, check the road reports. But if its open and you go, you will be amazed. It is truly spectacular.
Enjoy the time. It's my home state and one of the most beautiful places in the world.