What interesting stuff can I do in D.C. on a Monday?

I'm taking a weekend trip to Washington, D.C., very soon. I plan to attend some of the city's great museums on Saturday and Sunday. I was hoping to tour the Capitol as well, possibly on Monday... but my congresswoman's office has not gotten back to me about when or even if I'll be able to do that. I see that most of the museums are closed on Mondays. So I'm trying to figure out what, if anything, I could do that day. Right now I'm scheduled to return home on Sunday evening, but if I can find enough interesting stuff to do on Monday, I'll extend my hotel reservation another night, and change my train ticket to Monday evening. I can leave my luggage at my hotel during the day.

I'm thinking maybe I can just schlep around and look at monuments? I could also ride the Metro and take photos -- I do love the Harry Weese-designed station architecture. But I'm searching for other ideas as well.