If you want to be right downtown near the Mall and Smithosonians, then the choices would include the Williard (old, grand hotel, but rooms smaller than you would get in a newer hotel), Hotel Rouge.

But the choices expand greatly if you go a bit outside the downtown zone and plan to use the Metro -- which is extremely convenient and not a hassle at all. If so, then the choices run are
West End: Ritz Carlton, Fairmont, Westin Grand
Dupont Circle: Hotel Madeira, Rouge, or Helix (these 3 are Kimpton Group, very hip and 'W-esqe as gleff says)
Georgetown: Ritz-Carlton and Four Seasons