This is a fairly small and often ignored, though pretty interesting museum. It may not be a must-see for everyone, obviously, but I highly recommend it and it is right in the must-see area of Old Sacramento.
The emphasis is on the military history of California, from the Spanish settlement to the present day, but it touches on other aspects of the military in the US and the world as a whole. It includes some good displays on the US Civil War, especially the little-known role that California, then one of the newest states, played in the war, as well as WWII.
The California State Military Museum is small, modest, but still interesting. It has displays of uniforms, small arms, and equipment from the early Spanish settlers to the present day.