What to see at Buda Castle
Castle Hill which is a Unesco World Heritage site, rises 48 meters above the beautiful Danube River. Here you will find many medieval monuments and museums including the National Gallery and the Budapest History Museum.  The area consists of two parts, the Old Town and the Royal Palace. This is the site where in the 13th century the original castle was built. The Old Town is where the common people lived while the Palace area was reserved for the nobility.
There are many ways to get to the castle including good public transportation but you may opt to take the funicular railway by crossing the Széchenyi Chain Bridge.