The most obvious reason is: the Sea of Galilee is in Galilee. That allows Mark to have characters who are fishermen, and to stage scenes that involve boats.
Second, Galilee is near enough to Jerusalem that Jesus and his entourage can plausibly, in the world of the play, walk to Jerusalem, where the play concludes.
Third, the Pharisees are in Galilee, ready to oppose Jesus.
The play is set c. 30 CE, datable by the presence of Pontius Pilate. At that time, the Galilee was not a Pharisee stronghold. This changed after the Jewish War, when the Pharisees relocated their headquarters to the Galilee. They were there when Mark wrote in the early 90s CE. They oppose Jesus immediately. In the Gospel, the Pharisees and scribes are allies. I think of them as lay people and intellectuals (rabbis) of the same sect. Interestingly, Mark has the scribes as members of the Jewish Council (Sanhedrin). This is dramatic license that allows the scribes to serve as a bridge between the Pharisees and the Sadducees. Once the Jesus character arrives in Jerusalem, the chief priests (Sadducees) become a major enemy.
Mark’s audience was pro-Jesus. They would not have cared about the misrepresentation of the actual alliances on the ground.* Mark created a wall of opposition against his protagonist so that he took on the traditional tragic role of the lone individual against the powerful Establishment. As in the trial of Socrates, which must have been staged many times. Good playwriting.
So there are at least three good dramatic reasons for Mark to have Jesus manifest in Galilee.
*David Fitzgerald writes in Nailed (p. 94) that the alliance of the Pharisees and the chief priests/Sadducees in GMark is not realistic:
“The Gospels are also completely wrong about first century Jewish religious politics. The Pharisees and the High Priest were never in cahoots with one another. Nothing could be further from the truth – they
were bitter political enemies. In reality, most everyone in Judea hated the High Priest, who was both a Sadducee (the Pharisee’s political opponents), and a puppet appointee working for the hated Romans. The Pharisees regarded the Temple priesthood as mere ceremonial functionaries doing the nation’s spiritual grunt work, keeping the sacrifices going and maintaining the Temple.5 Even in the best of times the Pharisees seemed to regard most high priests as little more than trained monkeys, saying “a learned bastard takes precedence
over an ignorant High Priest.”6″
(References are #5 Maccoby, Hyam, The Mythmaker: Paul and the Invention of Christianity, Harper Collins 1987, pp. 26-27. #6. ibid, p. 23)