Performing at the beautiful neoclassical Nationaltheater, a component of the Residenz palace that has been restored to its 1830s grandeur, the Bavarian State Opera is one of the world’s great opera companies. Every year it mounts a full season of grand operas with the world’s greatest singers and a superlative orchestra. The productions are often anything but traditional, however. The Nationaltheater is also the home of the Bavarian State Ballet. Attending an opera or ballet here may be worth it just to sit in such a gorgeous space.