What place became the center of Christ's ministry during his Galilean ministry?

Galilee.

Specifically, the town of Capernaum in Galilee.

Matthew 4:12, 13 - Now when Jesus heard that John had been put in prison, He departed to Galilee. And leaving Nazareth, He came and dwelt in Capernaum, which is by the sea, in the regions of Zebulun and Naphtali,

This was a fulfillment of prophecy, as Matthew reminds his readers in verses 14-16.

For other references to the house in Capernaum to which Jesus and the disciples sometimes retired, see Mark 2:1 and 9:33.