You may just want to avoid Lafayette Square at night
The spirits of many people haunt the square, and for good reason: it was a notorious slave market in its day; the former Williams Slave Pen and Robey Slave Pens, which are currently occupied by lobbying groups, are quite close by. On dark nights, the clanking of chains and the screams of people can be heard. Richard Key, the son of Francis Scott Key, was also shot by Daniel Sickles in the square; he died later that night, but can sometimes be seen wandering near the spot where he was shot.
... and you might not want to stay too late at the Octagon House
This building has served many functions over the years. It was the home of presidents and vice Presidents (after the White House was burned down, James and Dolley Madison stayed here while the Downtown quarter was rebuilt); served as a tenement, following the absence of well-to-do owners; and a school for young girls, after a cloister of nuns took over. It was untended, but not completely derelict, before it was purchased by the American Institute of Architects in the early 20th century.
Through all that history, it is rumored to still be haunted by its original inhabitants: Colonel John Tayloe, of one of the noted Virginia families that made their money as planters, and two of his daughters. Strangely, both of the girls died just before or after eloping with men their father disapproved of, and both of them fell down the house’s remarkable stairwell to their deaths. The first intended to elope with a British officer, but her death cut that dream short; the second managed to elope with a young local boy, but when she attempted to reconcile with her father, she suffered the same fate as her sister. Staff and visitors to the house can hear a woman’s shriek toward nightfall, and later residents, as well as some visitors of the Madisons, reported seeing a woman’s body, crumpled at the foot of the stairs.