Stay in Fairfax or Chantilly, Virginia and drive to DC. 4 metro ticket may worth parking in DC already. If you stay for a week, you can buy 7-day metro for $15.
You should go to franklin d. roosevelt memorial and world war II memorial as well.
I like library of congress and national botanial garden too.
You can go for a day trip to luray caverns if you have time.
Steven F. Udvar-Hazy Center in Virginia is better than airspace musuem in DC. Parking $15, free entrance.