Most readers will already be aware of the NT Pod podcast on the question of Jesus’ birthplace by Mark Goodacre, and the response from Clayboy. I thought I’d chip in with my $.02 worth.
For me, the fact that Jesus was known as “Jesus of Nazareth” (such designations indicated one’s place of birth, as the case of Saul of Tarsus seems to confirm) is key evidence pointing to Jesus’ birthplace having been Nazareth. Although Matthew and Luke seem to agree (independently, for those who subscribe to the Q hypothesis) on Jesus having been born in Bethlehem, that is one of very few details these authors agree on when it comes to the birth of Jesus. Both are clearly engaging in strenuous and contrived attempts to have Jesus be born in Bethlehem and yet still account for his being known as “Jesus of Nazareth.”
I have some course notes on my web site about the problems historians face when dealing with the infancy stories in Matthew and Luke, for those who may wish to explore this and other related topics further.