A quick search on Hertz.com (rental car) shows a one way rental from the Washington Hilton HLE (pretty close to Chevy Chase) to Newport News (close to Yorktown) is about $180 (less if you have a discount code of some type) for a smaller-sized SUV like a Toyota Rav4. You can get by as little as $133 for a mid-sized sedan like a Toyota Corolla. I frequently use one-way rentals getting to/from a trip as the cost for a bus/plane/train ticket plus the cost of bringing the gear is usually only about 10%-15% than renting.
My point is depending on how much you want to do an "official" coast to and save time, this might be a compromise for you. It would take about 4 hours to drive there.
Can your friend in Chevy Chase just take you there if you pay the gas? That would be best.
Anyway, these are just some thoughts and no matter what option you pick, I hope you have a great trip.