Badlands NP provides views that are both visually harsh and beautiful. There is a loop road that will take you through the park and which will take at least 1-2 hours depending on how many stops you make. There is also an excellent Visitor Center which provides an excellent overview of how this scenery came to be. Allow another hour if you plan to watch the video.
Even though they aren't as visually as exciting as the Badlands, there is a very interesting Visitor Center in Wall for the National Grasslands program. We were surprised how interesting this was.
If you are interested in more recent history, there is also a unique historical landmark nearby, a Minuteman underground control center and missile silo. Tickets are needed for the underground tour, but it is a fascinating look into the Cold War and the people who kept their fingers on the buttons that could have taken us to real war.
In addition, nearby Wall has the Wounded Knee Museum, a sad look at our relations with Native Americans in the late 1800's. And, of course, there is always the tourist trap known as Wall Drug which is worth walking through once.