Iron Mountain Road continues straight into Custer State Park. Admission is $10 for a motorcycle, half the price of a car. I recommend taking the Wildlife Loop through the park, which winds slowly through the prairie where buffalo, bighorn sheep, pronghorn, deer, elk, coyote, prairie dogs, and numerous bird species roam free.
This may be one place that is better to visit outside of bike week, as the only wildlife I saw was a deer and this herd of wild burros, descended from a former trail ride pack that was set free. It's entirely possible that the constant rumble of loud pipes all week scared the other wildlife away from the road.
Contrary to what you see in the picture, the park recommends that you stay on the road with your vehicle. These are wild animals, despite how calm they often act. If you do encounter a herd of buffalo blocking the road, just sit tight and wait them out. They're bigger than you.