2. Sumeg CastleSumeg Sümeg Castle is a castle by the town of Sümeg, Veszprém county, Hungary.Built in the mid or late 13th century by Béla IV of Hungary, Sümeg Castle is situated atop a mountain called Castle Hill, 20 miles north of Lake Balaton. During its existence, it has been expanded several times. In the 15th century, it was fortified, and the second of two towers was built. It has been under siege several times, and has experienced two fires. Today, it is the main tourist attraction for visitors to Sümeg. From Wikipedia, the free encyclopedia.