Yeah, IAD is really about 45 minutes away by bus, but DCA is right along the subway system. If you can plan your trip so you go to DCA instead, do it.

I stayed in the Dupont Circle area years ago when I went with my parents, but when I tried to get to MAD via IAD and that flight cancelled, my girlfriend and I stayed in DC for a few days instead and stayed at the Capitol Skyline hotel (Washington DC Hotels, Washington Hotel - Capitol Skyline Hotel, Downtown DC Hotel near Smithsonian, Capitol Hill, Nationals Ballpark). Nothing too fancy, but the location you get for the money is pretty good without totally breaking the bank. It's between the Navy Yard and Waterfront stations, I'd definitely use the Navy Yard station - while the walk between there and the hotel is pretty good (I saw 2 corvettes pull out of a condo garage within 2 minutes of each other), on the other side between the hotel and Waterfront station is a little sketchy, especially at night. Otherwise, if you don't mind a hotel that looks like it was designed by Ikea a few years ago, go for it!