One way would be to follow the Lewis and Clark Route which goes through Sioux City. Last year I did a tour from Washington to Iowa intending on following the NT and L&C. I changed plans when I got into North Dakota and just used road maps to get to Iowa. I had started staying in motels at this point so it may not be of as much use if you are camping. I tried to describe the road surfaces and traffic and take photos of the roads. Here is a link to my journal.http://www.crazyguyonabike.com/doc/ttac
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.http://www.sddot.com/pe/projdev/docs/roadwaychar.pdf
Good luck with your ride.