The Gouda municipal museum occupies the Catharina Gasthuis, a medieval hospital complex that grew over several centuries into one of the more interesting historic buildings in the city. The collection covers local history, Dutch tiles, Gouda pottery (distinct from Delftware in its earthier palette), silver, and a collection of paintings from the 17th to 20th centuries. The building's chapel, courtyard, and apothecary room are highlights of the architecture alone. Not essential if your time is short, but good for understanding Gouda beyond its cheese.
Museum Gouda
Civic collection in a medieval hospital: Dutch tiles, silver, and paintings