The area around the White House is dead at night. I advise visitors staying in hotels who are coming for tourism reasons to say in the Gallery Place/Chinatown area, Dupont Circle, Georgetown, or Capitol Hill neighborhoods. There will be much more in the way of restaurants, bars, coffee houses, and shops, especially at night. In the daytime, I expect you'll be at museums, monuments, etc.

The W hotel is quite nice, though at the pricier end of the spectrum as one might expect.