We stayed 4 nights in Rapid City. It was a good location for what we wanted to do.
Beautiful sunrise.
We drove the southern, scenic route 44 from Rapid City to the Interior Entrance of Badlands

Grasslands
We had a cold, snowy day at the Badlands. We did the Door (.75 mile roundtrip) and Window (.25 mile roundtrip) trails. They were short, easy boardwalk trails. The boys wanted to do the Notch trail but the weather wasn't the best for a difficult 1.5 miles hike. It would have been prettier on a sunny day but still cool to see the rock formations.
The Door trail was nice because you could go out & explore around the area.
There were lots of overlooks along the scenic road. It was amazing how different the overlooks were.
We hiked a little in the Saddleback Pass. It was snowy pretty good then & was incredibly muddy so we didn't go as far as the boys wanted to go.
Yellow Mounds Overlook
Prairie Dog Town down Sage Creek Rim Rd