After reading Luke 2:4 I find myself assailed by the memory of David’s other residence. Bethlehem is where the king’s family was planted.

And Joseph also went up from Galilee, out of the city of Nazareth, into Judæa, unto the city of David, which is called Bethlehem; (because he was of the house and lineage of David:)

It was in Bethlehem that Ruth, a Moabite, David’s great grandmother, married Boaz.

Then it was said of Ruth:

Ruth 4:11

And all the people that were in the gate, and the elders, said, We are witnesses. The Lord make the woman that is come into thine house like Rachel and like Leah, which two did build the house of Israel: and do thou worthily in Ephratah, and be famous in Beth–lehem:

However, David’s name is also attached to fame and royalty via another city.

When David captured Jebus (יבוס yebûs) he named it Zion, and inherited the domain of Melchisedec, the ancient Salem (shalem שלם). This is the part of the hills of Moriah designated City of the great king. (Gen. 14:18, 2 Sam 5:6-7, 2 Chr. 15:2, and Psalm 48:1-2)

A Song and Psalm for the sons of Korah.Great is the Lord, and greatly to be praised in the city of our God, in the mountain of his holiness. Beautiful for situation, the joy of the whole earth, is mount Zion, on the sides of the north, the city of the great King.

There are two different Davidide cities and neither is Jerusalem.