Crowned by a filigreed spire and looking proudly back on 1000 years of history, the sandstone Münster was the church of the Diocese of Konstanz until 1821. Its interior is an architectural potpourri of Romanesque, Gothic, Renaissance and baroque styles. Standouts include the 15th-century Schnegg, an ornate spiral staircase in the northern transept, to the left of which a door leads to the 1000-year-old crypt. From the crypt’s polychrome chapel, you enter the sublime Gothic cloister. On cloudless days, it’s worth ascending the tower for broad views over the city and the lake.