[Robert A Cook PE]

Birth certainly at Bethlehem. But were they still at Betrhlehen when the Magi arrived?

The Magi then were told about the prophecy (Son of David... Bethlehem ... " but that doesn't mean that the family was still in Bethlehem when they (the Magi) visited, does it?

He did grow up in Nazareth, so at some point the family went back to there.

[Charles Henrickson]

The Magi then were told about the prophecy . . . but that doesn't mean that the family was still in Bethlehem when they (the Magi) visited, does it?

Almost certainly it does. It would be a very strange reading indeed of Matthew 2:1-11 to have several mentions of Bethlehem, including the magi receiving information to go to Bethlehem, and then have them go to some other unnamed place that is not Bethlehem.

He did grow up in Nazareth, so at some point the family went back to there.

Yes, but not until AFTER they fled Judea (where Bethlehem was), sojourned in Egypt for a while, and THEN returned, not to Judea, but to Galilee, to the city of Nazareth. See Matthew 2:22-23.