I just got back from South Dakota on Saturday. We drove this way on the way there and it was super boring! Made it to Billings the first night.
http://goo.gl/maps/kV4j6
On the way back we drove this way
http://goo.gl/maps/2bwOx and it was awesome. We got to stop at Devils Tower and also got to see some beautiful scenery. We were pleasantly surprised after being really down on how boring Montana was that the western side offered a very scenic drive and well worth the additional time in my wife and I's opinion (at this time our son just wanted to go home). We left really early from Rapid City on the way home (around 6:00AMish - we felt refreshed so it was time to go) and made it to Great Falls the first night.
That doesn't help you get into the States, but it lets you know a way into Montana to avoid.