Some said, "Hasn’t the Scripture said that the Christ comes of the offspring of David, and from Bethlehem, the village where David was?" (7:42). Does John's Gospel say where Jesus was born?

No. John's Gospel names Bethlehem only here, in the words of those who ask it (7:41-42), and it names no place where Jesus was born. In it Philip calls him "Jesus of Nazareth, the son of Joseph" (1:45), and in this chapter some ask, "What, does the Christ come out of Galilee?" (7:41). Matthew says, "Now when Jesus was born in Bethlehem of Judea in the days of King Herod" (Matthew 2:1), and Luke tells that Joseph went up "to David’s city, which is called Bethlehem, because he was of the house and family of David" (Luke 2:4), and of the birth there (Luke 2:6-7). Favor's chapter on Matthew 2 holds the promise pair from Micah 5:2 to Matthew 2:5-6, where the chief priests and scribes tell Herod the Christ would be born "In Bethlehem of Judea" (Matthew 2:5). Those speaking in 7:42 name no passage, and these notes don't name one for them. John's Gospel doesn't say whether they knew where Jesus was born, and these notes don't either.