Crowning the capital atop Castle Hill, Buda Castle presents an architectural melting pot, with Renaissance ruins around the foundations, a grand Habsburg-era neoclassical façade, and a stark communist-style interior. The palace is divided into three museums: The Hungarian National Gallery, the Budapest History Museum and the National Széchényi Library. You could easily spend the whole day just mooching around these three.
Time Out tip: Make sure to bring a camera – the views over the river and cobbled courtyards are something else.