'City of David' in the Bible

Shallum the son of Col-hozeh, official of the district of Mizpah repaired the Fountain Gate. He rebuilt it and covered it [with a roof], and set up its doors with its bolts and its bars, and [he rebuilt] the wall of the Pool of Shelah (Siloam) by the King’s Garden as far as the stairs that descend [the eastern slope] from [the section of Jerusalem known as] the City of David.

At the Fountain Gate they went directly up the steps of the City of David by the stairway of the wall above David’s house to the Water Gate on the east.