Castle Hill Funicular It's a steep walk up Castle Hill and for this reason a Funicular is available.  The funicular takes you to the entrance of Buda Castle.  I visited late afternoon on a cold day which meant it was empty but I'd imagine it gets busy during the summer.  You can either take a one way ticket up and walk down or get a return ticket.  The trip up Castle Hill probably takes less than 2 minutes. Hungarian National Gallery Located inside Buda Castle is the Hungarian National Gallery., Buda Castle, Budapest