I'm moved to and from DC a couple of times. I highly recommend the middle of the week and during the middle of the day, particularly if you are wanting to park a moving van on the side of the street. The beginning and end of the school year is also bad due to the number of schools in the area.

I don't know if I've ever had as much fun as navigating a 24' Budget truck through the streets of Adams Morgan, except maybe doing the same thing a few years earlier in Cambridge, MA...