The Gospel of Luke, at Luke 24:13-35, records that Jesus appeared to two disciples who were walking from Jerusalem to Emmaus, which is described as being 60 stadia from Jerusalem (10.4 to 12 km depending on what definition of stadium is used), after his resurrection.
Answer: The distance from Buffalo to Washington is 284 miles.
Driving between New York City and Washington DC. The driving distance is only 227 miles, but they are toll roads almost the whole way, so set aside at least $20-30 in addition to the fuel costs.