Minneapolis and Philadelphia are about 983 miles apart by road. Split the difference and you arrive near Detroit, the city closest to the halfway point between them. That puts roughly 11 hr 22 min of driving on the Minneapolis side and 9 hr 15 min on the Philadelphia side — the fairest single meeting point among the cities near the middle.
Over this distance most people will fly rather than drive the whole way. Detroit still makes a fair, central place for Minneapolis and Philadelphia to converge, splitting the travel instead of asking one side to cross the country.
If Detroit doesn't have what you're after, Cleveland and Chicago are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Minneapolis and Philadelphia.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.