The Mongolian Military Museum is a specialist stop, but a useful one if you are trying to understand Ulaanbaatar beyond the central temples and squares. Its collections trace military history from older steppe warfare into the twentieth century and the modern Mongolian armed forces.
Expect a local museum rather than a polished international blockbuster. The value is in the context: uniforms, weapons, photographs, and displays that show how Mongolia's strategic position shaped its modern state.