The answer
The Jews thought it right that God should be worshipped in the Temple in Jerusalem, because this was the only holy place in which sacrifices were offered. They didn't believe that other people could have different holy places, and they applied that especially to the Samaritans because of the enmity which existed between them and the Jews.
The Samaritans however had their own holy mountain.
When the Lord Christ spoke these words to the Samaritan woman, he was not alluding to a third place, and was not defining an alternative spot either, but was referring to the spread of the faith to the Gentiles.
That is, He was not singling out Jerusalem alone or Samaria as being places of worship, but was saying that faith was for all peoples and nations, and that worship could be performed in any sacred place on earth, but "the true worshippers will worship the Father in spirit and truth." (John 4:23)
The Lord Christ was not substituting one nation for another, but was in fact opening the door to all.
If He had meant that there was a third place, then it would have meant that the concept of God's 'chosen people' was to remain (and just apply to the Jews), but that it simply moved from one place to another, and that there was to be no general diffusion of the religion. This, of course, would have been at odds with what He said to His holy disciples: " Go into all the world and preach the gospel to every creature." (Mark 16:15), and " Go therefore and make disciples of all the nations, " (Matt. 28:19), also, "you shall be My witnesses in Jerusalem, and in all Judea and Samaria, and to the ends of the earth. " (Acts 1:8)
Yet the Lord Christ did not declare that Jerusalem was not to be considered holy, nor did He substitute some other place for it. The people of the whole world till this day go to Jerusalem and worship there.
The true worshippers of God are those who worship Him in spirit and in truth. And this was what Jesus meant by His words to the Samaritan woman, who considered that the hostility between the Jews and the Samaritans, and their different places of worship, were a barrier to her faith.
The place where worship is performed is not the most important thing, but what is important is that the person worships in spirit and truth, wherever he may be.
The true worshippers are those who worship God in spirit and truth, for they are the kind of worshippers the Father seeks. "God is Spirit and those who worship Him must worship in spirit and truth." (John 4:23-24).
So where is this 'third' place then? There is no indication, or definition or prophecy concerning it. It is rather an explanation of the true meaning of worship, and of not restricting it to a particular location.
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Thrice-Blessed Pope Shenouda III of Blessed Memory