One of the best kept secrets is that Washington DC is terrific during Labor Day week. All the families with kids have disappeared and the school groups haven't started. The only people there are retirees and people with little kids (but not too many of them.) I lived in the DC area for 30 years and worked right on the Mall for much of that time. Labor Day week was always my favorite. The one negative for you may be the weather -- it is frequently just as hot as August. But you would be in museums most of the time, so it wouldn't really matter.