When planning your travel to Charlottesville the closest international airports are Dulles airport outside of Washington DC (IAD) or Richmond airport (RIC). Please note that there is no direct public transportation from these airports to Charlottesville. There is an Amtrak train from Washington DC about 40 miles west of Dulles airport which departs from Union Station. It is easiest if you can plan to arrive directly into Charlottesville airport (CHO). A taxi from the airport to the University will cost approximately $25. Information on international airports with direct (non-stop) service to CHO can be found here:
http://www.gocho.com/routes-stops/
Dulles Airport (IAD)
Dulles is about 110 miles (2 + hours) by car from Charlottesville. IAD itself is 40 miles west of Washington, D.C. When you arrive at Dulles you can reach Charlottesville by train, bus or car.
Train
Amtrak does not service IAD or Washington International Airport (DCA). You have to go from these airports to Union Station in Washington, D.C. in order to take Amtrak to Charlottesville. Since DCA is right on the metroline it is the easiest airport to access Union Station.
Taxi from Dulles
You must arrange taxi service in advance.