Two museums that I have been to in recent years that cater brilliantly for musical instruments - and mainly instruments associated with traditional music:-

THE HORNIMAN MUSICAL INSTRUMENT COLLECTION in South London
see http://www.horniman.ac.uk/collections/musical.php
I was particularly surprised and delighted to see a beautiful kora made by Alhaji Bai Konte the father of my great friend from the Gambia Jali Sherrifo Konteh

and

THE BRUSSELS MUSICAL INSTRUMENTS MUSEUM
see http://www.mim.be/en
Apart from the building itself being really stunning, there is a really extensive collection of instruments in the galleries on several floors as well as special exhibitions and an impressive, varied programme of talks and concerts.
They give you headphones as you go in and as you stand in front of an exhibit, you can hear a good recorded example of that instrument being played. The kora that they had there was a rather inferior looking one made in Guinea Bissau, but as I stood in front of it, I was exhilarated to hear the playing of.....Alhaji Bai Konte!