The interesting part is that what is now
Appomattox on a map isn't actually
Appomattox Court House.
When a railroad between Lynchburg and Richmond came through sometime not long after the American Civil War and Reconstruction, the entire town of Appomattox packed up and moved about four miles south to be on the railroad line. This left old Appomattox Court House as a purely historical site, not to be marred by train tracks or U.S. 460 as it came through. And that's a good thing.
To visit the battlefield, take Virginia 24 north from modern-day Appomattox.