The route

We’ve laid out the travel route from Arlington, VA to the northern entrance to Yellowstone  (it’s the only one that’s guaranteed to be open–the other entrances may very well still be snow-covered).  Google Maps says that it’s 2, 231 miles–and 37 hours of driving.  We are going to take 9 days to do the drive.  Some of that time we know we will spend visiting family and friends  (including a stop in Milwaukee to visit Happy the Hippo) , but we’ve put aside 3 days to get from Milwaukee to Gardiner.  That give us 3 days to spend in the Badlands of North Dakota….now the question (and we’d love some advice) is where should we stop–what’s worth the time?