Business Insider has posted "10 overrated tourist attractions in the US — and where to go instead." For South Dakota, Badlands National Park is recommended over Mount Rushmore. This is correct. A drive through the Badlands (or possibly even Spearfish Canyon) is more scenic than Mount Rushmore (which I did not visit until my 14th-or-so trip to South Dakota). It also has its own gift shop and the chance to visit world-renowned Wall Drug on the way in or out of the park.
For Washington DC, they recommend Smithsonian museums over a non-tour visit to the White House. An extra benefit of the Smithsonian museums is that they are free. You can leave and go to another without wasting an admission fee. Two specific recommendations for Washington DC:
1. The National Museum of American History has a broad collection, including First Ladies' gowns, the original 15-star Star Spangled Banner, and Kermit the Frog (and once displayed the "puffy shirt" from Seinfeld). It's also about a block from the Ellipse view of the White House, so you can take any necessary pictures from there.
2. Out by Dulles Airport is the much larger Air & Space Museum: the Udvar-Hazy Center which basically has all the aircraft that were too big to fit downtown.