This cathedral runs an architectural gauntlet from the Romanesque (it dates from the late 13th century) to the Gothic and beyond to the baroque. The simplicity of the facade and clear lines are striking from the outside, but inside it will drive those who love the symmetry of the Romanesque style to despair as the nave is noticeably out of kilter with the sanctuary. Fifteenth-century wooden apostles peer down from pillars and there’s a baroque high altar and pulpit. To visit the Turmmuseum , a free-standing tower that provides grand views over the city’s rooftops, you need to ask inside the Stadtmuseum. Someone will take you up there, but only in good weather.