The Wildlife Museum (formerly known as the Hunting Museum) is on the 2nd floor of the Baigal Ordon (Nature Palace) on the street leading to Gandan Khiid. The museum has well-presented taxidermy displays of Mongolia's wildlife, as well as displays of centuries-old trapping and hunting techniques that are used by both nomads and urban cowboys.
It’s usually locked, so ask for the key from someone downstairs.