Jodi Magness has a chapter on synagogues.
Like church, synagogue means an assembly of people. Their meeting place is called a church or synagogue by extension. Archeology looks for the buildings, the meeting places.
The fact from this chapter that stood out for me is that we have many examples of synagogues after 70 C.E. but only a handful before then. There are several theories about when Jews began the institution of the synagogue. The most conservative is that synagogues date clear back to the time of the first temple. There is no archeological evidence for this and textual evidence is slight and has to be interpreted in an unnatural way.
Another view is that Jews began to form synagogues during the Babylonian exile. I used to think this was true. It makes sense that with the loss of the Temple, Jews would have to find a new institution. But there is neither archeological nor textual evidence for this. The same with the idea that the synagogue arose at the time of Ezra and Nehemiah.
A more compelling theory is that synagogues existed first in Egypt among the Jewish settlements there. There are inscriptions about Jewish “prayer houses” in Alexandria and other Egyptian cities. A prayer house is not exactly the same thing as an assembly or synagogue. But it could be another way of speaking of the same thing. Sometimes churches are called houses of prayer.
So even though the Gospels and the Book of Acts feature synagogues and we know that they existed both in Jerusalem and in the Diaspora at the time, we have few archeological remains. The real heyday of the institution seems to be after the fall of Jerusalem in 70 C.E.
But we do have some remains of early synagogues. Herod the Great set aside rooms at Herodium and Masada for this use. But such royal synagogues may not represent the usual village or neighborhood synagogue.
In 1913 the Theodotus inscription was found in Jerusalem. This inscription says that a synagogue there was dedicated for the purpose of “the reading of the Torah and teaching the commandments” and that it included “the hostel, and the rooms, and the water installation for lodging needy strangers.” In other words, the place existed for education in Judaism and for hospitality to those visiting Jerusalem for the festivals.
On the Sea of Galilee we found synagogue buildings in Gamla and Migdal (or Magdala, home of Mary of Magdala or Mary Magdalene). These synagogues had lines of benches under a pillar-supported roof. They had no Torah shrines, and they were not oriented toward Jerusalem like post-70 synagogues. The Migdal synagogue was just found in 2009 and the full report on the find has not come out. But there was a large stone block in the middle with carvings. Carved on one side of the block was a Menorah. It is one of very few examples of this symbol before 70 C.E. and the only one found in a synagogue.
One interesting fact is that the institution of the synagogue and rabbi did not develop together. Today a rabbi usually presides over or serves a synagogue. But rabbis in the first century were teachers and scholars who did not necessarily have a role in the synagogue. Inscriptions show that the leading person at a synagogue was called in Greek an archisynagogas. Whether this person functioned as an administrator or liturgist or something else, we do not know.