Klaus Wanderer
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This place was the absolute highlight of my trip to the city, I loved everything about it and anyone even remotely interested in architecture and/or art will love it
The admission ticket is about 3.5 euros and you will be spending about half an hour inside depending on how many pictures you want to take. In some areas they don't allow pictures though (the better rooms, of course).
In the most famous room of the palace there are some beautiful stained glass windows and a five minutes explanation will play for you
There is also a museum at the top floor that was, sadly, closed at the time of my visit