Despite its name, the Chinese Association of Museums is a grouping of Taiwan's museums. There's some English on the website, but the most interesting and useful section - listings of museums by region, focus and status (government-supported or private) with a search function - is Chinese only. In all, the site has details of 461 museums.
The Council of Cultural Affairs, a central government agency, has a few details in English here. Taiwan's best-known collections include the National Palace Museum, National Taiwan Museum and the National Museum of Taiwan History. Less conventional but no less worth visiting are the 921 Earthquake Museum and the Museum of Drinking Water.