The Bible does not tell us where Zechariah and Elizabeth lived, however Church tradition believes they came from the town of Ein Kerem which is indeed in the hill country for Judah.
After the Feast of Pentecost had ended, and his time of service had been completed, Zechariah returned home to his home town of Ein Kerem in the hill country of Judah…..TJB 1:9
The journey to Ein Kerem would have taken Mary at least three days to travel depending on the route she took. If you went around Samaria like many of the Jews did when travelling to Samaria it would have taken her at least four days. And had gone through Samaria which is over a 100Km journey it would have taken her at least three days.
It is also very unlikely that a young girl around the age of 16(?) would have gone alone. She would have traveled with a few companions for safety as there were thieves that patrolled these roads looking for easy targets.