The metro is awesome. We did everything in between the flight in and out on public transport. It takes you everywhere you need. The metro stops right outside of Arlington. We took a bus from the metro to Mt Vernon. The bus ride was a little longer but direct. The kids actually loved seeing Virginia that way.
I would warn that you should try getting all of your museum tickets staring now. CV19 is still significantly limiting hours and availability. Trumps stupid tantrum still has the Capitol under lockdown.