I know of no exhibits organized explicitly around mechanical music,
but when in Beijing you should not miss the enormous clock collection
in the Forbidden City.  The emperors of China had a fascination with
mechanical devices, and amassed large numbers of very exotic timepieces,
many of foreign origin and dating to the 18th century.  There are
several rooms of them on display, and some are breathtaking.  It has
been some years since I visited, so I do not recall if there are any
automata.

A. B. Bonds