Just from personal experience, you might try a Kimpton Hotel (
www.kimptonhotels.com) They have several in the DC area. From personal experience I have stayed in the Hotel George near Union Station and also Hotel Monaco and Hotel Lorien in Alexandria, Va. The Lorien is a couple of blocks from the metro and Monaco is a few blocks further down the street but they have a trolley that runs back and forth.
Kimpton hotels can be pricey but I find they offer a lot of specials, especially if you sign up for their email alerts.
I believe the Hotel Morrison in Alexandria is also a bit like a bed and breakfast.
Good luck and enjoy!