dc traffic is really bad and outside of paid parking garages, there aren't any spaces in DC, so metro is definitely the way to go.
metro does do day and week passes, not sure where mooby's coming from with that:
Metro - Fares - Purchase - SmarTrip Card & Pass Options
not cheap though. i remember when day passes were under $5. getting old.
hit air and space, natural history, anything else is up to you. lots of people like the holocaust museum, but if you've watched a ton of the history channel (when it was 24/7 ww2 docus) there may not be much new there.
as for food, i can't really help there. don't eat at the museums though, unless $12 happy meals sounds like a good deal.
outside of DC there are a lot of great parks/hiking/boat stuff/etc depending on what you want to do.