I was a little taken back by the Greyhound buss idea too. Most of the stops ar enot in the best parts of the towns the buses stop. Rent a car and see the country. I drove across country with my 9 and 12 yr old granddaughters 12 years ago and we stoppted whenever we saw something that caught our interest. It took us 6 weeks, 28 states and 8,000 miles. Get in touch with AAA and join for a small fee and have them plan a trip for you which is free with membership. We stayed at Motel 6 mostly as they had pools LOL for the kids and clean and reasonable prices. March is iffy weatherwise for D C area, can be beautiful can be miserable. If I had 3 weeks I would go between Williamsburg and Lancaster as people have suggested these places. If flying into D C, have AAA plan trip from D C to WIllimasburg to Lancaster back to DC. I have lived in D C area my whole life and still enjoy going sout or north of D C. Have a great trip. Take care.
Linda