If I were to do it again I would have followed US 2 from Williston to Minot, North Dakota and then started south and east from there. You might check out US 52 which heads SE out of Minot and connect with US 281, which I rode on for a while. The part of 281 that I rode on had a nice shoulder.
South Dakota DOT has a bicycling section with a Roadway Characteristics Map, which I found very useful. Here is the link.
Good luck with your ride.