I have spent a lot of time in South Dakota and the Black Hills, not just on motorcycle trips, but on family vacations. There is an incredible amount of stuff to see and do there.
Some other posters have suggested a lot of the obvious stuff; let me point out some of the more out-of-way attractions.
1. From the Badlands leave by Sage Creek Road, near the southwest corner of the scenic loop. It will bring you out on SD44 near Scenic, a near ghost town that used to be a popular stop for bikers and tourists, and a favorite watering hole (Longhorn saloon) for bikers and local Indians. This road is good, wide gravel.
2. South of Scenic, go up on Sheep Mountain Table, if your vehicle has some ground clearance. There are some great panoramas all around, including an old bombing range.
3. Drive across Cuny Table to the town of Buffalo Gap. If it is open, stop at the Cuny Table Cafe for an indian taco, and chat with Nellie Cuny (last August, at least, she was still alive, according to a local in Scenic). She is a great and gracious lady who knows about everybody on the rez, and most of the old ranchers in the surrounding area.
4. From Buffalo Gap, cross SD79, go through the eponymous Gap, and up Red Valley Road through the back side of Wind Cave natl. Park via Red Valley Road, and into Custer State Park near the SE corner near the buffalo corrals. On the Custer Wildlife Loop, you will probably see buffalo up close, semi-wild burros, and, at a distance, antelope. The back country scenery in these two areas (Red Valley and the Wildlife Loop) is the most beautiful in the Hills, IMO.
5. Visit Hot Springs for the Mammoth Site park and the hot water park.
6. Rochford is an old mining town in the back country of the southern Hills. Moonshine Gulch Saloon is a good stop for a beer and a beverage.
7. Sugar Shack, on US 395 at Merritt-Estes road is another great burger stop.
8. The store at Cheyenne Crossing, at the head of Spearfish Canyon, has the best Indian tacos in the Hills.
9. In the NW Hills, drive up to the fire tower at Cement Ridge for some more great panoramas, then drive up (down?) Sand Creek Canyon, "The Grand Canyon of the Black Hills", to Beulah, on I90.
10. For some really incredible back-country prairie scenery, drive up north of Wall to Creighton and Pedro, in the Cheyenne River Breaks. You may run across some abandoned missile silos, and a control center. The roads up in there are excellent gravel, but have a good map, like the Delorme atlas.
The entire SW quadrant of South Dakota has some incredible areas to explore. Many are accessible only by an off-road bike or atv, but the areas above can all be reached by car.
