Mainz's natural history museum sits in the old city centre and is a useful change of register after the cathedral, Roman stones, and Gutenberg material. The collection is strongest on the natural world of Rhineland-Palatinate: fossils, minerals, mounted animals, and exhibits that explain the Rhine landscape around Mainz.
It is not a blockbuster museum, but it is a good wet-weather stop and a solid choice with children. The building itself also helps: the museum occupies a former convent complex, so the visit folds a bit of Mainz's older urban fabric into an otherwise science-focused hour.