As an alternative to Dulles Airport you could try flying into Baltimore / Washington International (BWI), then heading into Baltimore to take the Amtrak Northeast Regional train to Newport News which is ~30 miles from Yorktown.

You could do pretty much the same flying Dulles then getting to Washington DC Union station, but the airport -> train connection would be shorter and cheaper in Baltimore. Not sure what airfare differences, if any there are between the two airports, but for domestic flights BWI is the 'cheap' airport for the DC region.

<gripe about US train system>
The sad part is that there's a train station at BWI airport, but you can only have your bike boxed and checked as baggage on that train line and there's no baggage service at the BWI train terminal.
</gripe>