Many of the arguments over the original location of Solomon's temple revolve around various Biblical references. These do make it quite clear that it could be nowhere else but in the City of David--that crescent-shaped ridge forming part of the Mount Moriah prominence. The City of David was also known as Zion and again and again the scriptures make clear that God resided in Zion and spoke from Zion. In that place (THE PLACE, HaMakom as it was known to the patriarchs), at the Gihon Spring, David had erected a temporary tent where he housed the ark of the covenant and the sacred objects and, importantly, where he had Solomon anointed for kingship. That tent, of course stood at HaMakom and marked the spot that had become so recognised through the ages, at Gihon Spring.
But--the most telling reason that the Temple was located here (in my view)--is the spiritual reason. For the Temple had to have 'living water' at its location in order to represent the life of God flowing in and from the Presence of God--as the video below explains. (Alternatively ou can view it on YouTube at https://www.youtube.com/watch?v=VCOp7M62NUI )
You can also read my book 'THE PLACE HaMakom; where Jerusalem's temples stood' and discover more. Buy it now on Amazon USA here or in Australia here