In Helena, the state capitol. There is a place called Parrot Confection that makes its own candy and ice cream. It is a well preserved soda fountain from the turn of LAST century and serves whatever you would like. It has some great stuff but has a pretty limited menu beyond ice cream.
In my opinion, the most memorable thing that we saw in Montana was the Charles Russell Museum and Studio in Great Falls which is several hour north of Bozeman. His artwork is outstanding and we spent a lot more time there than we planned. We stayed at the Great Falls Inn which is affiliated with Montana's largest hospital, The Great Falls Clinic. The rooms were large and very reasonable.
I would recommend Jaker's for their steaks, chops and fish, generally trout.
In Butte, the "hometown specialty" is the pasty, yes pretty similar to what you'll find in the UP. Why not? They were both areas settles with Cornish miners.
If you are expecting Chicago variety in Montana, I think that you'll be very disappointed with your time in Montana. On the other hand, I have yet to find as good of pie in Chicago as I had throughout Montana.