Go to the door, and lift up the arm to unlock the door. Open it, and find yourself looking out the green door near the big stone ball by the dam.
Head back inside. Lift the block on the other door as well, and you'll see you're within the stone cutout on the other side of the dam. Look at the Mayor's desk, and turn over the compass inside the little box to find a hint - in my playthrough, it was "Rhode Island", but "North Carolina" , "Texas", "Arizona", "Missouri" and "Colorado" have also been seen; other choices can be generated, perhaps at random.