Someone in The New Testament mentions two places where one ought to worship God. Jesus says that in the Messianic Era neither place will be where one ought to worship God. Which are these two places by name, and—according to Jesus in the New Testament—where will be the one place by name where the true worshipers will worship God in the Messianic Era?
The reference is presumably to this passage in the Gospel of John:
Our ancestors worshiped on this mountain, but you [plural—i.e., the Jews] say that the place where people must worship is in Jerusalem.”
Jesus said to her, “Woman, believe me, the hour is coming when you will worship the Father neither on this mountain nor in Jerusalem. You [plural—i.e., the Samaritans] worship what you do not know; we worship what we know, for salvation is from the Jews. But the hour is coming, and is now here, when the true worshipers will worship the Father in spirit and truth, for the Father seeks such as these to worship him. God is spirit, and those who worship him must worship in spirit and truth.” (John 4:20–24)
The two places mentioned here as places to worship God are:
Mt. Gerizim, which is near Sychar, the town in which Jesus had this conversation with a Samaritan woman (see John 4:4–7 and a map here). This is the most sacred mountain in Samaritan tradition, and the place where Samaritans were especially to worship God.
The Temple Mount in Jerusalem. In Jewish tradition, this is the mountain where God is to be worshiped with sacrifices and offerings.
Jesus does not mention any physical location where people will worship God in the Messianic Era. Rather, he says that true worshipers, in a coming hour (i.e., a time that had almost come), and even in the present (at the time he was speaking, and not only in some future Messianic Age), will worship the Father (God) "in spirit and truth."
In other words, the "place" that Jesus says true worshipers will worship God, and do worship God, is not a physical location, but an inner state of spirit and mind.