All three synoptics say only that he took them up a high mountain. Tabor is the tradition, attested from the fourth century and carrying a basilica since the sixth, and it is where this dataset puts the Transfiguration — marked traditional, because that is what it is. The objection is old and reasonable: Tabor is nowhere near Caesarea Philippi, where Peter's confession has just happened six days earlier, and Hermon is. The tradition chose the mountain that could be climbed and built on.
OrthodoxWiki · Transfiguration