The two Hungarian cities that are solutions to the crossword are Eger and BUDAPEST. Eger is a city in northern Hungary, located on the Eger Stream. It is known for its thermal baths, baroque architecture, and its castle. BUDAPEST is the capital and largest city of Hungary. It is located on the Danube River and is home to many cultural attractions, including the Hungarian Parliament Building, Buda Castle, and the Szechenyi Chain Bridge.