The Museum zu Allerheiligen occupies a former Benedictine monastery founded in 1049, and it is one of the most rewarding regional museums in Switzerland. The collections span medieval art, prehistoric archaeology, and natural history, and the presentation is serious without being academic. The Roman-era finds from the Rhine crossing at Schaffhausen are particularly good.
The monastery cloister is the real architectural prize: a Romanesque arcade garden that has survived largely unchanged for nearly a millennium. Even if you skip the collection, walk through it. The admission covers both the permanent galleries and the cloister, and the whole visit takes two to three hours if you give it proper attention.