There is not really a museum or collection at hand in Amsterdam.
Perlee is the major street organ owner in Amsterdam, and they do own
a small museum.  However, it's impossible to find any information at
their web site about opening hours, an so on.  My advice is --

You will probably arrive at Amsterdam/Schiphol Airport.  From there
you can easily travel by train to Utrecht, which is a short trip (about
20-30 minutes, I guess, only 40 or 50 kilometers).  From the railway
station in Utrecht it's a short walk (15 minutes) to the famous museum,
"Van speelklok tot pierement", one of the major museums for mechanical
music.  The museum is in the center of Utrecht.  Easy to find.  If
needed I could mail you a map with the route from the station to the
museum.

You will be able to see, and hear (guided tours in English) a lot.
Dutch street organs, of course, but much, much more.  Utrecht may not
be as famous as Amsterdam, but it's a very old and beautiful city as
well.  Worth a visit.

Jan Kijlstra
(And yes, I'm Dutch.  But no, I'm not living in Utrecht ;-) )