You ask a loaded question.  There are lots of things to do while wandering
around DC.  The most impressive thing I've found is the differing
architectures throughout DC proper and some of the outlying areas, such as
Georgetown.  The National Cathedral is especially impressive - and I think
may have been completed in the past decade.  I don't remember in what
century construction began.  While I'm not Episcopalian, the Easter
services were incredible!