If you include the Badlands Nat'l Park in your itinerary (and you should), add a day for that. Also, about an hour or so west of Rapid City is Ft. Laramie. Well worth a visit and you can see most of the Fort in a couple of hours.
As for camping, I don't know how hard it might be to get a site right now, but look at Custer State Park. A great park and very close to Mt. Rushmore.
oh yeah! will bill and calamity jane. town is pretty good! could spend a day there easily. it is also quite the hike upto the graves of the two. in the bar is the chair he was shot in.
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Full Timing - Salem Villa Estate - 392FLFB - Purchased July 29th 2010