Budapest Castle Funicular took its first trip from the banks of the River Danube up to Buda Castle in 1870. It was the brainchild of Odon Szechenyi, son of Count Istvan Szechenyi of thermal bath fame. The funicular was destroyed in a bombing raid in World War II along with most of the city. Two meticulously accurate vintage reproduction cars ply the 311-foot track today. 1,200 Hungarian Forint ($4.25) for a single ticket; 1,800 Hungarian Forint ($6.37) for a return ticket.