Two other thoughts:

1) The Dulles branch of the Air and Space Museum (the Udvar-Hazy center) runs a bus directly from the airport bus stop. I'm not sure what the schedule is, but you might be able to find it on line.

2) The Kennedy Center is worth going to at night, but doesn't usually have day time events of any interest. (There are some weekend matinees.) Personally, I don't think much of its architecture but those who are more into modernism may disagree. It won't work with an 8 (or even 9) p.m. flight, but they do have a free performance every night at 6 at the Millennium Stage. And, by the way, it is actually quite easy to get to by public transit. It's a pleasant walk from the Foggy Bottom metro station - and they also run a free shuttle bus to/from the station (about every 10 minutes, from noon to midnight). I usually walk and take the bus back to the metro if I'm on my own and walk both ways if I'm with somebody else.