Budapest is the kind of European city with both a rich cultural history and a thriving modern art scene. Considered one of the most beautiful cities in the entire region, its extensive World Heritage Site includes the banks of the Danube, the Buda Castle Quarter, the Andrássy Avenue, Heroes' Square and the Millennium Underground Railway, the second oldest in the world. That's not mentioning the more than 80 geothermal springs and the #1 bar scene in Europe.
One place we want to recommend is the Mucsarnok and its institutions. Here's the museum's history from their website:
The Műcsarnok (“art hall”) was founded in 1877 on the initiative of the Hungarian National Fine Arts Association. The original building was situated at 69–71 Andrássy Street, now home to the University of Fine Arts. The exhibition hall on Heroes’ Square was erected in 1896 for the millennium celebrations, and was designed by Albert Schikedanz. Today the hall operates on the pattern of the German Kunsthalle: it is an institution run by artists that does not maintain its own collection. The three-bayed, semi-circular apse houses a roofed exhibition hall that allows in light through the roof. Since the building was renovated in 1995 the Műcsarnok has welcomed visitors and leading Hungarian and international contemporary artists alike, mediating and representing modern artistic tendencies whilst not maintaining its own permanent collection.