Hard to read maps:
The most direct route would take Jesus, his mother, and the disciples 14 km to Cana. Using the SWP data, we see a 2.5 km trail descend to the northeast from Nazareth to Reina (see Map 4C), whose ancient name is not known. (A Sepphoris aqueduct starts in Reina.) From Reina, at 300 m above sea level, they could continue northeast about 1.5 km to a point near Gath Hepher, skirting to the east of Sepphoris.
Strange, J. F. (2014). The Galilean Road System. In D. A. Fiensy & J. R. Strange (Eds.), Galilee in the Late Second Temple and Mishnaic Periods: Life, Culture, and Society (Vol. 1, p. 268). Minneapolis, MN: Fortress Press.