Assuming you're doing this now (and not in January!), I'd recommend the northern route. Mt. Rushmore and the Badlands are totally worth it since you're driving right through there. Madison's a good place for a short stop. Chicago's worth a couple days if you have time. Once you're east of Chicago you have a lot of choices for routes...especially if you're open to leaving the Interstates.

I've driven Kansas City to Washington DC and back a couple times. I've never liked I-70 at all...it's a beat-up old highway, heavily clogged with trucks, and full of speed traps across Ohio and Indiana. As you're driving, you're either thinking "they should really repair this highway" or you're sitting in a construction delay because they are repairing it!

As much as I think coming south for some burnt ends at LC's could be fun, if you're only doing this once...stay north. Better roads, less traffic, and I can't imagine the cops in South Dakota are quite as thick as they are in Ohio.