The remains of Hammath-Tiberias extend from the hot springs (el-Hammam) to the southern boundary of ancient Tiberias, on the western shore of the Sea of Galilee. In the Talmud, the place is identified with Hammath (Joshua 19:35), a fortified city of the tribe of Naphtali:

"Hammath-Hammatha" (J.T., Meg. 1, 70a)

This identification is not certain, however, because the excavations and a survey of the Hammath area uncovered no remains earlier than the Hellenistic period. Hammath is mentioned many times in the Mishnah. Tiberias and Hammath were originally two separate cities, each surrounded by a wall of its own

"Rabbi Jeremiah said ... from Hammath to Tiberias - a mile" [J.T., Meg. 2:1-2])

Subsequently, however, they were united, apparently in the first century CE:

"Now the children of Tiberias and the children of Hammath again became one city." (Tosefta, 'Eruv. 7:2)

In the liturgical sources (Mishmarot 24), Tiberias was known as Ma'uziah after the priestly order that had settled in Hammath. Tiberias was forbidden to the priests because it contained a cemetery. When Tiberias became the seat of the Great Yeshiva and the Sanhedrin in the third century CE, and the spiritual center of the Jews of Palestine and the Diaspora, the suburb of Hammath shared its prominence. With the abolition of the patriarchate in about 429 CE, Hammath began to decline, but it continued to exist as a city, supporting itself with its profitable hot springs. The Jewish community remained in the city throughout the Arab period until its decline in the Middle Ages.

• Annotated Google Map of Tiberias and environs from biblewalks.com
  Annotated Google Map of Tiberias and environs
  
  biblewalks.com
• Plan of synagogue IIA from Stern et al (1993)
  Hammath-Tiberias: plan of synagogue IIA
  
  Stern et al (1993)