It is questionable if the location is the correct one, but the name is certainly interesting, the place maybe not the original, but stands in a place that maybe the original, nobody can be sure...but just is worth the visit if you are in the market.
The synagogue church is located in the heart of the old city and is only worth a visit if you are already planning on walking the old city. It's simple and questionable whether or not Jesus was ever there.
I have my doubts about the authenticity of the place. The barrel shaped roof is probably Byzantine, much later than the ime of Jesus.
Also-Jewish synagogues are always oriented towards Jerusalem. As Nazareth is North of Jerusalem it should have face south- but it does not. Being conveniently located next to a large church one can see why it was...
Not worth a journey by itself, but if you are in Nazareth and you are visiting the Basilica of Annunciation (which is very worthy of a visit), this place is a 5 minutes walk from it, uphill thru the market.
After you visit the Latin Church of the Annunciation, go up through the market place above the church and follow the shops turning first to the left then to the right and again right into a small courtyard that leads past another church on your right and the church-synagogue is to the left. It is said to be built on...