'City of David' in the Bible

Shallun son of Col-Hozeh, head of the district of Mizpah, worked on the Fountain Gate. He rebuilt it, put on its roof, and positioned its doors, its bolts, and its bars. In addition, he rebuilt the wall of the Pool of Siloam, by the royal garden, as far as the steps that go down from the City of David.

They went over the Fountain Gate and continued directly up the steps of the City of David on the ascent to the wall. They passed the house of David and continued on to the Water Gate toward the east.