In 1710 Prince-Bishop Johann Franz Schenk von Stauffenberg, perhaps tired of the dinginess and rising damp, swapped the Altes Schloss for the dusky-pink, lavishly baroque Neues Schloss. A visit to the now state-owned palace takes in the extravagant bishops’ apartments replete with stucco work and frescos, Bathasar Neumann’s elegant staircase, and gardens with inspirational lake views.