It is hotly debated whether or not there were any synaoguges in Jerusalem during the Second Temple period. However, both the Jerusalem Talmud and the Babylonian Talmud give a different impression:
"There were four hundred and eighty synagogues in Jerusalem, each of which had a bet sefer and a bet talmud. The bet sefer was for [the study of] the Bible, and the bet talmud for [the study of] the Mishnah, and Vespasian destroyed them all" (y. Megillah 3.1.73a).
A similar claim is made in b. Kethuboth 105a, claiming the number of synagogues in Jerusalem was 394.
Do these late texts give sufficient evidence that there were synagogues in Jerusalem during the Second Temple period, before 70AD? I seem to recall that in the Essene sector of Jerusalem, there is archaeological evidence for mikvehs, which may suggest the existence of a synagogue there. I will research this further.