Taiwan Theater Museum is Yilan's most distinctive cultural museum, focused on Taiwanese opera, puppetry, costumes, stage craft, and local performance traditions. It is not a giant national museum, but that works in its favour: the subject is specific, regional, and easier to connect with than another general history display.
Check whether performances or demonstrations are scheduled before you go. Even without one, the museum helps explain why temple festivals and street processions in Yilan can feel so theatrical: music, masks, gods, and travelling stages all belong to the same world.