Visiting the Badlands this year is a VERY good idea. With all of the rain we've had, the landscape is lush and green and is quite beautiful against the contrasting colors of the buttes and canyons. As far as location, you may wish to consider staying in the Medora area, which is located at the South Unit of the park. The drive between the North Unit and South Unit is about 82 miles via Hwy 85. The area around Medora has the most accommodation options. You can find a list of options at: www.ndtourism.com/listings/places-to-stay .
You'll find lots of things to see and do in Medora, such as the Medora Musical. More information about this can be found at: www.medora.com.
If you are looking for information about General George Custer, you can find this at: http://www.history.nd.gov. You can find a map of the Custer Auto Tour in North Dakota by contacting the National Park Service, 701-623-4466.
ND Tourism Division
You'll enjoy Custer House and Fort Lincoln. There is a lovely trolley ride from Mandan down there if you'd like something a little different. I'd also stop at Fiesta Villa (not great quality lately) which is where the Bismarck train depot was or across the street at the Peacock (way better food and atmosphere and is connected to the train depot underground.....was quite useful during prohibition for those trains coming from Canada, especially since the politicians stayed at the hotel there and likely enjoyed those banned goods from Canada). That is where the news of Custer's death was first reported and the Bismarck Tribune got the scoop. The Heritage Center is under renovation still, but it might be worth a stop to see if they have any of the Custer era historical documents on display.
This might be an interesting read for you: https:/…20lecture.pdf
And Standing Rock (which is lovely scenery down to the Casino there) might be worth a drive for you too.