The Museo de Historia Natural is run by the University of Santiago de Compostela and gives the city a useful science stop away from the cathedral crowds. Collections cover animals, minerals, fossils, plants, and Galician natural environments, with enough variety to hold attention even if you are not a specialist.
It is especially useful for families or for a wet afternoon, which Galicia supplies often enough. The museum also broadens the city beyond pilgrimage and stone architecture, reminding visitors that Santiago is a university town with scientific collections as well as sacred history. Pair it with a walk through the nearby green spaces.