The West Garrison is located inside Blackrock Depths, and is accessible from the East Garrison and the Ring of the Law (after defeating the ring challenge). Note that the West Garrison and all areas beyond are locked by a mechanism located in the East Garrison, which requires the Shadowforge Key to operate.
The West Garrison is the first area that is always required to pass through to eventually get to the last areas of the instance, the Imperial Seat and the Molten Bridge. It is home to the terrible General Angerforge and numerous Dark Iron dwarf minions. A tunnel leads directly from the garrison to the Manufactory.