San Jose and Washington are about 2,415 miles apart by road. Split the difference and you arrive near Oklahoma City, the city closest to the halfway point between them. That puts roughly 28 hr 28 min of driving on the San Jose side and 24 hr 6 min on the Washington 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. Oklahoma City still makes a fair, central place for San Jose and Washington to converge, splitting the travel instead of asking one side to cross the country.
If Oklahoma City doesn't have what you're after, Kansas City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between San Jose and Washington.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.