In Tihany, the Benedictine Abbey, founded in 1055, perches on a peninsula poking out into the lake, projecting its baroque splendor. It’s full of fancy frescoes, and you may catch a glimpse of a beaming bride and groom walking down the front steps. The adjacent Abbey Museum can give you the full (hi)story, such as the fact that King Karl Habsburg IV and Queen Zita were interned here in 1921 by the Entente Powers prior to their exile to Madeira.