God did not reveal everything at once to the Prophets in the past. Revelation from God is a progressive revelation. Lets see some examples-
The Law was a progressive addition: God gave few laws to Noah after the flood (Genesis 9). God then gave circumcision law to Abraham (Genesis 17). At last, the complete law was given in a written form to Moses.
Messiah was not clearly revealed in OT: For the Christians, the New Testament is the truth for interpreting the Old Testament. The NT is the final revelation of who the Messiah is and gives us a clear picture of the Messiah, not a vague and shadowy picture like the OT. The name of the Messiah as "Jesus" was not clearly predicted in the OT. If the name of Messiah was clearly written in OT, I believe there is higher probability for the Jews to believe that Jesus is the Messiah. The OT did not clearly mention that Messiah will be crucified, though the NT says the prophecy is hidden in Psalms 22 and others.
Applying the same concept to the Temple, we can infer that God did not reveal the chosen site for the Temple at once to Moses.
How the Temple site was chosen in Jerusalem: In 1 Chronicles 21, David aroused the anger of the LORD by counting the fighting men in Israel. The Lord sent Gad, David's prophet to inform the punishment from God. God sent a plague on Israel and sent an angel to destroy Jerusalem.
Then the angel of the Lord ordered Gad to tell David to go up and
build an altar to the Lord on the threshing floor of Araunah the
Jebusite. So David went up in obedience to the word that Gad had
spoken in the name of the Lord. While Araunah was threshing wheat, he
turned and saw the angel; his four sons who were with him hid
themselves. Then David approached, and when Araunah looked and saw
him, he left the threshing floor and bowed down before David with his
face to the ground. David said to him, “Let me have the site of your
threshing floor so I can build an altar to the Lord, that the plague
on the people may be stopped. Sell it to me at the full price.” (1
Chronicles 21:18-22, NIV)
David then decided to built the Temple there at the threshing site of Araunah the
Then David said, “The house of the Lord God is to be here, and also
the altar of burnt offering for Israel.” (1 Chronicles 22:1, NIV)
The Bible doesn't clearly mention why David chose that place for the Temple site. There was probably some divine understanding given to David that God has chosen that site for the Temple or David was divinely inspired because he was a man of God. We can see how God approved the alter built there by sending a fire.
So David paid Araunah six hundred shekels of gold for the site.
David built an altar to the Lord there and sacrificed burnt offerings
and fellowship offerings. He called on the Lord, and the Lord answered
him with fire from heaven on the altar of burnt offering. (1 Chronicles 21:25-26, NIV)
And later, when Solomon built the Temple there, God approved it.
The Lord said to him: “I have heard the prayer and plea you have made
before me; I have consecrated this temple, which you have built, by
putting my Name there forever. My eyes and my heart will always be
there. (1 Kings 9:3, NIV)