Not what you asked for but...
The Mickelson Trail will get you up from Edgemont, SD, take you right past Crazy Horse (you can literally see it from the trail), and bring you to Hill City. If you really want to see Mt. Rushmore you can spend a couple of nights in Hill City and do a loop day ride to the monument. There is a cool back road from Hill City to Keystone. It follows the historic rail line that runs steam train rides between the two towns. Plan your ride so you are on the road while the train is making one its runs to Keystone. The tracks cross the road in several locations. Pretty cool experience. Then you climb (steeply) up SD 244 to the monument and continue on it back towards Hill City. There is a nice commercial campground (Crooked Creek) in Hill City that is right along the trail.
You can then continue on the Mickelson to its northern terminus in Deadwood, head over to Spearfish, which has the nicest municipal campground I have ever seen, and head west into WY for Devil's Tower. Knowing what I know, I could exit the trail at the Engelwood trailhead, take U.S. 14A to Cheyenne Crossing, then Savoy then down Spearfish Canyon to the town of Spearfish.