In my opinion, skip Wall which is famous for it Drug Store. The store is nothing more than a tourist trap. We stayed 2 nights at the KOA in Interior. While not a fan of KOA, it was a nice place.
For Badlands, it can be a drive through visit or you can take several nice hikes early in the morning.
We highly recommend the Minuteman Missile Historic Site. Arrive early and sign up for the visit to the launch site. They only take 6 persons per visit. Very interesting!
The Custer area has so much to offer, I would spend most of your time there.