Time Out says
Crowning the city atop Castle Hill, Buda Castle is one of the city’s most recognisable monuments. It dominates the cityscape with its neoclassical Habsburg-era grandeur and reconstructed copper-green dome (the original was damaged during the Second World War). Fittingly for such a grandiose landmark, the castle terrace boasts sweeping views over the Chain Bridge, Hungarian Parliament and the rooftops of Pest.
After being razed and rebuilt over the centuries, you can see history written in Buda Castle’s walls and rooms with traces of its Renaissance, Ottoman, Habsburg and Communist past. The complex is now split up into a handful of excellent museums. The Hungarian National Gallery occupies the main wings facing the river and displays an extensive collection of Hungarian art from Medieval triptychs to avant-garde 20th-century works. The southern wing is home to the Budapest History Museum which charts the city’s tempestuous past from prehistory to communism, while the western wing encloses the National Széchényi Library.