In the synoptic gospels we find two birth narratives, that of Matthew and that of Luke, Mark has no birth narrative, nor does John.
In Matthew, Mary and Joseph live in Bethlehem where Jesus is then born. Matthew makes clear that this birth in Bethlehem is to fulfill a prophecy from Micah 5:2. Then, the Magi come and ask Herod where is the King of Israel. The Magi visit the baby Jesus in a "house, " presumably their home in Bethlehem and then return without warning Herod. Joseph is then warned by an angel in a dream to flee Bethlehem and Herod to Egypt. Herod orders all of the children below the age of 2 killed (sound familiar?). Then, after Herod dies, Joseph has two dreams, one telling him to return to Israel, and a second warning him not to go back to Judea (Bethlehem) but to go to Galilee, specifically the town of Nazareth.
So, in summary, Matthew reconciles the discrepancy as follows: Mary and Joseph live in Bethlehem where they give birth to Jesus, they then flee to Egypt, and upon returning to Israel, they settle in Nazareth.
Luke also tries to reconcile this discrepancy, but in a vastly different way. In Luke, Joseph and Mary live in Nazareth. The Angel Gabriel comes to Mary and announces the birth of Jesus, the Son of the Most High, Messiah. When it actually comes time for the birth of Jesus, Luke tells the story of a Census ordered by Caesar Augustus and carried out by Quirinius the governor of Syria. To register for this census, Joseph, from the tribe of Judah and of the House of David had to return to the town of David, Bethlehem. It is while Mary and Joseph are in Bethlehem registering for the census that Jesus is born.
So, in summary, Luke reconciles the discrepancy as follows: Mary and Joseph live in Nazareth, but are summoned to Bethlehem to register for the census, Jesus is born, and then they return home to Nazareth.
Same question, different answer depending on which evangelist you ask. What say you?