Chicago and San Diego are about 1,732 miles apart by road. Split the difference and you arrive near Denver, the city closest to the halfway point between them. That puts roughly 19 hr 15 min of driving on the Chicago side and 17 hr 28 min on the San Diego 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. Denver still makes a fair, central place for Chicago and San Diego to converge, splitting the travel instead of asking one side to cross the country.
If Denver doesn't have what you're after, Albuquerque and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Chicago and San Diego.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.