There is a lot of South Dakota that isn't part of the Black Hills. The parts of interest to a random traveler are a bit more spread out though. This page covers assorted other parts of South Dakota, starting with its largest city - Sioux Falls. If you've ever wondered if there actually is a Sioux Falls in Sioux Falls - there is - but it is called the Falls of the Sioux (just to be different). There is a very nice park here with assorted trails, bridges and overlooks along both sides of the river.
North and slightly west of Sioux Falls is the small town of DeSmet which would never have ended up on our web pages if Laura Ingalls Wilder hadn't lived there. In DeSmet proper are actually homes that Laura Ingalls Wilder and her family lived in. Just outside of town is the Wilder Homestead Museum which doesn't have original buildings but it has period buildings that have been moved there or reconstructed. That makes it into one of those living history museums but it's still a pretty neat place to visit. Plus, what else would you be doing in DeSmet if not visiting these sites?
There are a few different style of homes on the site as well as several barns, a reconstructed church and schoolhouse. There's a handful of livestock (and sleeping cats) if you have a small child to entertain. It can get quite hot here on a sunny day, even in September. Bring water.
North of DeSmet is the thriving metropolis (in South Dakota terms) of Aberdeen. Aberdeen has all the services you haven't seen in several hours or more if you've been driving around the Dakotas. They also have a mini tourist attraction in Wylie Park just north of the city. L. Frank Baum spent a fair bit of his life in Aberdeen so a section of Wylie Park is themed after the Wizard of Oz books/movie. There are assorted other children's playgrounds themed after other fairy tales as well. You can even follow the yellow brook road, but you'll probably get stuck at the tin man slide like we did.
In the middle of South Dakota is Pierre, the state capitol and not really all that notable otherwise. We didn't find a whole lot else to see and do here but if you're visiting the area it is worth noting that the time zone line between Central and Mountain runs right down the center of the Missouri River (and thus the city).
Southwest of Pierre is the Badlands National Park. There's a scenic loop through the park that parallels part of I-90. Be warned, there are almost no stores, restaurants or gas stations out here other than in and around the town of Wall.
The badlands is mostly a driving park with a lot of scenic overlooks to stop at. Since most of the formations are very delicate there are no trails or direct access to them. There are some short boardwalk trails that wind through them in the eastern portions of the park and a very few longer trails across the grasslands.
The badlands are incredibly rich in fossils and the visitor center contains as much information on this as it does on the geological formation. The Badlands are known for mostly Oligocene mammals which is a bit of a change from all the dinosaur sites in Montana and North Dakota. If you want your toddler to be the only toddler on the plane home who knows what a Mesohippus looks like, this is the place for you!