Well, the Cabelas parking lot in Mitchell, SD is free, if you don't count how much you might spend shopping in their store.
My wife and I often stay overnight at the Rest Stop along I-90 at Chamberlain, SD. This large rest stop sits a bit farther than most off the interstate, high on a hill overlooking the Missouri River, and has one of the prettiest views that you'll see along any interstate highway. Although the Interstate rest stops in SD all say that overnight stays are prohibited we've never had any trouble in that regards, and there is even a highway patrol office at located at this particular rest stop, along with a nice Lewis and Clark exhibit.
John