Built in 1748-49, this* is the oldest house in the Bronx, and "was the scene of military maneuvers and intrigue" during the Revolutionary War. Here are some great photos of the well-maintained interior, which has served as a museum of 18th-century life since 1896.
* The L-shaped structure on the left is the original house. You can't tell it's L-shaped in this photo, though. This bird's-eye view and this photo of the front of the house should make things a bit clearer.