Yes John the Baptist did visit Galilee. In Matthew 4:5-10, Jesus finds out that John has been incarcerated in Galilee so he would obviously have visited Galilee. Jesus goes to Galilee to visit John in verse 12.
John the Baptist did indeed visit Galilee but did not live there. In fact, John the Baptist go beheaded by Herod Antipas, the ruler of Galilee. Keep in mind that John the Baptist is not the same person as the apostle John.
