Jerusalem in King David’s time
Immediately after conquering Jerusalem, King David made it the capital of Israel. The walls built by the Jebusites were still used, with a few expansions towards the north. David did not expel the Jebusites but instead appointed them as officers in his administration.
The City of David is now the village of Silwan, located south of the Old City of Jerusalem.
David’s Jerusalem was called the City of David, and was way smaller than present-day Jerusalem, housing a population of only about 1000-2000. The city was surrounded by high, thick walls originally built by the Jebusites. The main structures of the City at that time were a Palace, a Millo, and the walls of the City. The neighboring Gihon Spring watered the City and it was surrounded by valleys on almost every side that served as natural shields.
The Palace
King David lived in a palace that was built for him. The Bible says,
“Now Hiram king of Tyre sent envoys to David, along with cedar logs and carpenters and stonemasons, and they built a palace for David.” (2 Samuel 5:11)
The palace, whose remains constitute the Large Stone Structure now, was built outside the city walls, to the north, on a high platform. King David resided here. However, when the Philistines intended to invade the palace in order to murder King David, he retreated back into the fortified City. The Bible says about this,
“When the Philistines heard that David had been anointed king over Israel, they went up in full force to search for him, but David heard about it and went down to the stronghold.” (2 Samuel 5:17)
Stepped Stone Structure
Apart from the Palace, relics of a historical structure, now called the Stepped Stone Structure, are also present that lead up to the Palace. There is a lot of controversy as to the function of the Stepped Stone Structure. The most widely accepted one is that it is the Millo that was mentioned in the Hebrew Bible. The Bible says,
“Then David dwelt in the stronghold and called it the City of David. And David built all around from the Millo and inward.” (2 Samuel 5:9)
The City of David that gave birth to Jerusalem extended over only a few acres, compared to the huge size of Jerusalem today, which amounts to thousands of acres! It’s actually pretty astonishing when you see the size of the City of David on a map!
References
http://www.aish.com/jl/h/cc/48936837.html
https://www.esv.org/resources/esv-global-study-bible/illustration_10_jerusalem-in-the-time-of-david/
http://www.generationword.com/jerusalem101/20-david-palace.html