Beer-loving, fast-driving, palace-dotted Bavaria, Germany, home of Oktoberfest, BMW, and Neuschwanstein (the castle that inspired Disney), is toasting its centennial as a free state this year.

Other beer-focused attractions in Bavaria include the oldest monastery brewery in the world at Kloster Weltenburg on the Danube, founded in 1050 and still operating; the underground catacombs and ...