You can find the information about Jesus being born in Bethlehem in the following passages:
* Matthew 2:1-6: This passage explicitly states that Jesus was born in Bethlehem of Judea during the time of King Herod. It also references a prophecy from the Old Testament (Micah 5:2) about a ruler coming from Bethlehem.
* Luke 2:4-7: This passage describes Mary and Joseph traveling from Nazareth to Bethlehem to be registered for a census because Joseph was of the house of David, which originated in Bethlehem. It then states that while they were in Bethlehem, Mary gave birth to Jesus.
These are the primary sources in the New Testament that describe Jesus' birth in Bethlehem.