The driving distance from Louisville, Kentucky to St. Joseph, Missouri is approximately 410 miles (660 km).
I-64 W → I-70 W (via Indianapolis, Terre Haute, Effingham, St. Louis, Columbia, Kansas City metro, then US-36 W / I-229 N to St. Joseph)
Fly: SDF → MCI (1h20m) + 1h drive to St. Joseph = ~4h door-to-door. Often cheaper than driving solo if booked ahead.
St. Joseph — Pony Express start, Jesse James end, massive livestock history — worth the trip across the corn belt.