Nazareth is the traditional boyhood home of Jesus (Matthew 2-4). The centerpiece for Christian pilgrims is the Basilica of the Annunciation, which enshrines a traditional spot where the angel Gabriel appeared to Mary and announced that she would have a child and should name him Jesus (Luke 1).
Adjacent to the church is a baptistery built over what is thought to be an ancient Jewish ritual bath (mikvah), and an excavation of the ruins of ancient Nazarene homes.
Even further north is the Church of St. Joseph, which is built over a complex of chambers traditionally identified as the workshop of Jesus' father, Joseph.
The existing city of Nazareth is (as it is recorded as being in Jesus' day) a bit of a dump. But as is so often in Israeli cities, as you rise into the hills above the lower city, Upper Nazareth is much more residential and upscale.