No, the backside of Mount Rushmore National Memorial doesn't have the presidents' posteriors carved in granite as some tourist memorabilia would have you believe. What the area does hold, however, is one of the best hike-able summits in the Black Hills.
Mount Baldy, behind Mount Rushmore, offers sweeping forest views with granite outcroppings, Black Elk Peak and, if timed correctly, the 1880 train chugging through the hills. The large granite uplift is a great place to have a picnic lunch and let the scenery sweep over you.
Not to be confused with Old Baldy near Spearfish, the Mount Baldy Hiking trail starts at the Wrinkled Rock Climbing Area parking lot about a mile west of the Mount Rushmore profile view parking lot on Highway 244. The trail does require some rock scrambling and light non-technical climbing. If you aren't comfortable doing those things, you shouldn't try to reach the summit.
The hike to Mount Baldy is only 1.5 miles, but getting on the correct trail can be difficult, since trails spider web throughout the area to several rock climbing routes. During the hike, keep Mount Baldy in your view to help guide you. Looking east from the parking lot, you will see Mount Baldy's distinctive granite dome with large boulders perched on the summit.
Leave the parking lot and head east, then go south on the gravel path past several climbing areas. You will come to an interpretive sign talking about the rock climbing area in what is called South Seas.
Just south of the sign, you should see a path that leads you east down a gully. Follow that path for roughly 5 minutes. You will walk through a small aspen grove at the bottom of the gully.
There the path intersects: take the path that leads south and then east. From there, the path is fairly straightforward. Follow the markers with the hiker on them. You will traverse around to the east side of Mount Baldy to reach the summit.
Once at the base on the east side of the mountain, you will notice a large but gradual granite flow up the side of the mountain. Follow it up, taking the path of least residence along the way.
There will be spots where you have to squeeze through a small crevasse or scramble up a quartz band. Move slowly and deliberately to find the easiest way up. If you reach small grassy ledge with a tree on it, you are almost to the top.
At the summit, take a seat and enjoy the view and be sure to sign the summit register, which is located in an old ammunition canister.