I lived near Washington DC from April 1985 till June 1989. I lived in Woodbridge, VA; then 2 different places on Fort Belvoir; then Manassas, VA. We went into Washington DC almost every week-end and many times through the week. Even back then, there was NEVER a good time to go! It was horrible then (anytime of the year, week-end, week-day, day or night) ... it's only gotten worse! Pick your time and just go!
FYI, we lived there for over four years, went to DC all the time to see something different, traveled the area as much as possible, and STILL didn't see everything we wanted. (in 4 years!) There's just way to much there! Pick your time and pick your attractions! And good luck!
(And I was in the Army during most of that time, and got to see and go places that the average "citizen" doesn't get to go too!) Awesome 4 years, but REALLY am glad to be back home in Indiana again and have no desire to ever go back again.