In short
Capernaum—which had a synagogue (Mark 1:21), a Roman barracks (Matthew 8:5–13), and a tax booth (Matthew 9:9)—was located at what is today called Tell-Hum, about four kilometers west of where the Jordan meets the Sea of Galilee.
The city of Capernaum was located on the site that is today known as Tell-Hum approximately four kilometers west of where the Jordan river flows into the Sea of Galilee on its northwestern shore. At the time it was one of the most important cities in Galilee. There was a synagogue (Mark 1:21), a Roman barracks (Matthew 8:5–13), and a tax booth (Matthew 9:9).1
13 And leaving Nazareth he went and lived in Capernaum by the sea, in the territory of Zebulun and Naphtali,