The Western Hill was not settled until the area around the Eastern Hill (the City of David) began to fill up.
People then began moving outside the walls of the City of David and across the Central Valley to the Western Hill. When the Assyrian Empire invaded northern Israel in 723, BC many of the Jews from Israel fled south into Judah and settled in Jerusalem. They also settled outside the walls of the city on the Western Hill.
Hezekiah eventually built a wall around this new western suburb in preparation for the Assyrian attack of Judah in 701 BC. (Part of this “Broad Wall” can still be seen.) This portion of the city fell in 586 BC to the Babylonians along with the rest of the city. When the exiles returned it was settled again after the days of Nehemiah.
By the time of the New Testament, the Central Valley had been filled in and the city had again expanded to cover the Western Hill. Herod’s palace was built along the west wall on the Western Hill, as were many of the wealthy residences of New Testament Jerusalem, including the mansion of the high priest. Jesus would have been brought to the Western Hill to appear before Annas and Caiaphas. It is quite possible that the Upper Room, used during the Last Supper and on the Day of Pentecost, was also on this Western Hill.
Today the Christian Quarter and the Armenian Quarter inside the walls of the Old City are on the Western Hill.
The area south of the Armenian Quarter outside the walls is today called Mount Zion, and it is also part of the Western Hill. (In scripture, Mount Zion originally referred to the Eastern Hill, or the City of David. Mount Zion then began to refer to the northern part of Mount Moriah, or the Temple Mount. Early Christians of the Byzantine and Crusader periods wrongly identified the southern part of the Western Hill as Mount Zion, but it maintains that name to this day.)