The Freer Gallery is a good collection of East Asian art.
It's not all great; I wasn't deeply impressed by some of the pottery. (I had visions of people digging up American forks and claiming them as art, five hundred years from now.) But there are a few really beautiful specimens, and that's not the main focus of the gallery.
I was deeply moved by the long Japanese folding screens in one room of the gallery. They're the parallel-development form of tapestries or murals, and many of the screens are both exquisite and dramatic.
When we visited, a large part of the Whistler collection was in a room closed for renovation; it was a shame, because I got a glimpse through the barrier of a very neat set of paintings.
The Peacock Room, however, was open, and this must be seen to be believed. There's a cute story, which I won't ruin here, but the long and short of it is that Whistler ended up moving a privately commissioned room into its permanent location at the Gallery here.
While you're on the Mall and looking for pretty things, stop by the Freer Gallery. It's worth it.