BlueSharpie

I have lived in Rapid for about three years now (originally from Louisiana) and the tips you’ve gotten have been pretty spot on (other than about winter weather- while higher elevations in the hills get a good bit of snow, Rapid City has one of those microclimates due to winds and being protected by the Black Hills that, while it does snow during winter, it melts in a day or two because it doesn’t stay cold here like it does in the eastern part of the state. It may snow one day, and be 55° the next day, thanks to the Chinook winds. It’s really not too bad- at least not in my experience thus far.)
Regarding restaurants in Custer, a previous poster is correct that Black Hills Burger is no more. However, I recommend a place called The Custer Wolf to fill the void. They have great burgers and a fried green bean appetizer that even my green bean-hating daughter loves. I’ve never had a bad meal there.
I’m not sure when your exact dates are, but fall foliage should be great in Spearfish Canyon and elsewhere around mid-September.
Enjoy the trip! Can’t go wrong with Custer State Park, Badlands, Mt. Rushmore, and Spearfish Canyon. This is a lovely part of the world.

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Awesome, thanks!

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My dad drives one of his antique motorcycles across the country every couple of years in the Motorcycle Cannonball. LINK They generally avoid interstates. Maybe digging around online for some of the old routes they have used will give you some ideas?