Washington DC is an awsome city for a visitor. The majority of the museums are free. The monuments are worth seeing. Lots of tours or just wandering. There are always events being held on the mall. There is public tranport out to surrounding areas.
Do some GOOGLEing and look to see what is heppening in DC during your dates.
http://washington.org/
We did a bike tour and had a lot of fun.
Don't discount DC!