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:
"And David dwelt in the stronghold, and called it the city of David. And David built the city round about from the Millo inward. And David became greater and greater, for The Lord, the God of hosts, was with him. And Hiram king of Tyre sent messengers to David, and cedar trees, also carpenters and masons who built David a house. And David perceived that The Lord had established him king over Israel, and that he had exalted his kingdom for the sake of his people Israel." (2 Samuel 5:9-12 RSV)
"David built houses for himself in the city of David; and 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, for The Lord chose them to carry The Ark of The Lord and to minister to Him for ever." And David assembled all Israel at Jerusalem, to bring up The Ark of The Lord to its place, which he had prepared for it. And David gathered together the sons of Aaron and the Levites" (1 Chronicles 15:1-4 RSV)
"And it was told King David, "The Lord [see The Logos and Rock Of Ages] has blessed the household of Obed-edom and all that belongs to him, because of The Ark of God." So David went and brought up The Ark of God from the house of Obed-edom to the city of David with rejoicing ... And they brought in The Ark of The Lord, and set it in its place, inside the tent which David had pitched for it; and David offered burnt offerings and peace offerings before The Lord." (2 Samuel 6:12,17 RSV)
"Then David slept with his fathers, and was buried in the city of David. And the time that David reigned over Israel was forty years; he reigned seven years in Hebron, and thirty-three years in Jerusalem. So Solomon sat upon the throne of David his father; and his kingdom was firmly established." (1 Kings 2:10-12 RSV) (see Bible Places)
"Solomon made a marriage alliance with Pharaoh king of Egypt; he took Pharaoh's daughter, and brought her into the city of David, until he had finished building his own house and The House of The Lord and the wall around Jerusalem." (1 Kings 3:1) (see Layout Of Solomon's Temple and Solomon's Kingdom)
"Then King Solomon assembled the elders of Israel and all the heads of the tribes, the leaders of the fathers' houses of the people of Israel, before King Solomon in Jerusalem, to bring up The Ark of the covenant of The Lord out of the city of David, which is Zion." (1 Kings 8:1 RSV)
"This same Hezekiah closed the upper outlet of the waters of Gihon and directed them down to the west side of the city of David" (2 Chronicles 32:30 RSV) (see Hezekiah's Tunnel)
"He prayed to him, and God received his entreaty and heard his supplication and brought him again to Jerusalem into his kingdom. Then Manasseh [see Kings of Israel and Judah] knew that The Lord was God. Afterwards he built an outer wall for the city of David west of Gihon, in the valley, and for the entrance into the Fish Gate, and carried it round Ophel, and raised it to a very great height; he also put commanders of the army in all the fortified cities in Judah." (2 Chronicles 33:13-14 RSV)
Fact Finder: Was King David's birthplace, Bethlehem, also known as the city of David?