if you are lazy - use the elevator. entry fee is 500 HUF. marvellous panorama.
Cross the Danube through this bridge from St. Stephen's Cathedral to the foot of the funicular for Buda Castle, or vice-versa.
You can pay to go to the top level or stay on the ground level for free! While looking at the cafe go to the left. There is a small opening where you can get to a ledge to overlook the city for free!
Enjoy sightseeing but have a drink or lunch somewhere else - as everything is unreasonably expensive inside and around the castle area.
