The Hall of Gears is located within Gnomeregan, and lies just beyond the Clockwerk Run. It has one upper level, which is completely taken over by irradiated troggs; and a lower level, which holds puddles of radioactive fallout, numerous oozes, poison elementals, and a mini-boss Viscous Fallout.
The Hall of Gears' upper level has two exits: the first, to the southeast, is a dead-end hallway featuring Blastmaster Emi Shortfuse and her collapsing-tunnels event with the first mini-boss, Grubbis; the second, to the southwest, leads to the Clean Zone and the Dormitory. The lower level has one entrance (on the south, from the Dormitory), and one exit (to the west, a winding tunnel leads to the Launch Bay.
Jumping from the upper to the lower level will not kill you, but you will likely aggro mobs when you land.