Antwerp, Belgium: MAS - Museum aan de Stroom

This isn't just a museum. It's a building filled with museums - one per each floor. And there are 10 floors; you can do the math. 

The subject matter is rather wide-ranging when it comes to Antwerp, and the architecture is interesting. While each of the museums has an admission charge, you can go on the outside of the building without a fee. That way you can work your way in a circular walkway to the very top, where you'll have a good view of the city around you.