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Chris,
Sounds great! If you have the flexibility, you might want to add up to a day in the Black Hills. Having lived there four years I can tell you all the great roads and sights to see but the majority of the twisty scenic roads run north and south up and down the Black Hills which doesn't move you toward Billings very fast.
I'm emailing you some directions for the best roads linking Rapid City to Mt. Rushmore to Spearfish Canyon to Devils Tower. That is a 3.5 hour leg without stopping but the roads are worth it! If you can spend more time there let me know and I'll give you more places to see like Crazy Horse Monument, Custer State Park, Sylvan Lake, etc...
As far as places to stay in SD, there isn't much along the interstate between Sioux Falls and Rapid City (except billboards for Wall Drug which is near the Badlands)
Have fun!
Dave McFaddin
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