Hartford and Los Angeles are about 2,510 miles apart by road. Split the difference and you arrive near Kansas City, the city closest to the halfway point between them. That puts roughly 24 hr 24 min of driving on the Hartford side and 28 hr 24 min on the Los Angeles 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. Kansas City still makes a fair, central place for Hartford and Los Angeles to converge, splitting the travel instead of asking one side to cross the country.
If Kansas City doesn't have what you're after, Oklahoma City and Omaha are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Hartford and Los Angeles.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.