It looks like you're focusing on Central Europe and environs. Lucky you - two months!
Amsterdam, as you probably already know, is one of the top cities in Europe for museums (along with Paris). IMHO, I would say that Berlin, Budapest and Prague, while very interesting from a historic viewpoint, are not known so much for their museums, generally speaking (disclaimer: I have not been to Berlin, but have a trip scheduled for there in October, so have been researching). Though I would highly recommend the Communist Museum in Prague and the Terror Museum in Budapest; I though they were very interesting. The museum of Cubist Art, if you like that kind of thing, in Prague, was good, especially when you follow it up with coffee and cake in their cafe (ideally on the balcony, so tourists can take pictures of you).
Bruges is just plain cute, but actually has a couple of nice museums and a reputed (disputed?) Bosch. A lot of people don't like Brussels, but my entire family really enjoyed the city, and the Art Museum is quite good. Several cities in the Netherlands and Belgium are worth seeing and have good museums or other locations of art, like the Ghent Altarpiece in Ghent (the Adoration of the Mystic Lam, by van Eyck), which has national significance to the Belgians.
Are you planning any time in the countryside? Especially for a trip of your length, you might consider mixing it up a bit by spending some time in a small town or village.
Enjoy!