BY WAY OF
I walked into the room and sat down by the fire place.
They ran out of the burning building.
He walked toward the City Hall.
You can go by way of the Panama Canal.
IN ordinarily refers to place or position.
INTO ordinarily refers to motion or action.
I saw him go into the director’s office a few minutes ago.
The went into the building an hour ago.
She is going into her mother’s room.
Tony went into that building ten minutes ago.