The great city of Chicago was sadly left out of the big US history tour. The data base for the National Register of Historic Places included Chicago in a separate directory, rather than under Cook County. And thus we missed them. Sorry. But Go Bears!
You can't have a US tour without Chicago, so I computed an optimal side-trip hitting all of its sites from the registry. Well, all except the Chicago Harbor Lighthouse, since it is a bit chilly to swim in the harbor at most times of the year. The shortest-possible walk through the 359 sites takes 328,006 meters, so a little over 200 miles.
After building machinery to solve the 49,603-stop tour, handling Chicago was a snap. The full computing time was a little over a minute on my Mac Mini.
You can click here for an interactive Google Map of the tour, or here for a list of the stops in the optimal order.