The earliest City of David was located on the southeast ridge of the Jerusalem plateau, with the Tyropoeon Valley to the west and the Kidron Valley to the east. Only a few acres in total, it actually covered a much smaller area than what later came to be known as the City of David section of Jerusalem.
As first established, the City of David consisted of David's palace, which overlooked the tent that David had set up to house The Ark Of The Covenant
(Solomon later built the original Temple of God there - see Temples). South of the palace was the citadel and the city itself. (see diagram below)
References to the City of David from the pages of Bible History:
"David then took up residence in the fortress and called it the City of David. He built up the area around it, from the supporting terraces inward. And he became more and more powerful, because The Lord God Almighty was with him. Now Hiram king of Tyre sent messengers to David, along with cedar logs and carpenters and stonemasons, and they built a palace for David. And David knew that The Lord had established him as king over Israel and had exalted his kingdom for the sake of his people Israel." (2 Samuel 5:9-12)
"After David had constructed buildings for himself in the City of David, he prepared a place for The Ark of God and pitched a tent for it. Then David said, "No one but the Levites may carry The Ark of God, because The Lord chose them to carry The Ark of The Lord and to minister before Him forever." David assembled all Israel in Jerusalem to bring up The Ark of The Lord to the place he had prepared for it. He called together the descendants of Aaron and the Levites." (1 Chronicles 15:1-4)
"Now King David was told, "The Lord [see The Logos and Rock Of Ages] has blessed the household of Obed-Edom and everything he has, because of The Ark of God." So David went down and brought up The Ark of God from the house of Obed-Edom to the City of David with rejoicing.... They brought The Ark of The Lord and set it in its place inside the tent that David had pitched for it, and David sacrificed burnt offerings and fellowship offerings before The Lord." (2 Samuel 6:12,17)
"Then David rested with his fathers and was buried in the City of David. He had reigned forty years over Israel - seven years in Hebron and thirty-three in Jerusalem. So Solomon sat on the throne of his father David, and his rule was firmly established." (1 Kings 2:10-12)
"Solomon made an alliance with Pharaoh king of Egypt and married his daughter. He brought her to the City of David until he finished building his palace and The Temple [see Layout Of Solomon's Temple and Solomon's Kingdom] of The Lord, and the wall around Jerusalem." (1 Kings 3:1)
"Then King Solomon summoned into his presence at Jerusalem the elders of Israel, all the heads of the tribes and the chiefs of the Israelite families, to bring up The Ark of The Lord's covenant from Zion, the City of David." (1 Kings 8:1)
"Solomon reigned in Jerusalem over all Israel forty years. Then he rested with his fathers and was buried in the city of David his father." (1 Kings 11:42-43)
"It was Hezekiah who blocked the upper outlet of the Gihon spring and channeled the water down to the west side of the City of David." (2 Chronicles 32:30) (see Hezekiah's Tunnel)
"And when he prayed to Him, The Lord was moved by his entreaty and listened to his plea; so He brought him back to Jerusalem and to his kingdom. Then Manasseh [see Kings of Israel and Judah] knew that The Lord is God. Afterward he rebuilt the outer wall of the City of David, west of the Gihon spring in the valley, as far as the entrance of the Fish Gate and encircling the hill of Ophel; he also made it much higher." (2 Chronicles 33:13-14)
Fact Finder: Was King David's birthplace, Bethlehem, also known as the city of David?