With a bit of time on my hands today, I have been delving into the internet a bit. I came across this gem of a site. The site has a wonderfully extensive list of cultural places to visit in Taiwan, extending well beyond the usual advertised sites. I know not all of these places are for children, but as a parent I try to give my children as broad an experience as I can. I think this site is a fantastic resource.
Look at the things you can choose from! The Swine Museum, the Firefly Museum, the Penghu Lifestyle Museum, the Dough Figurene Museum... Taiwan is full of wonderfully unusual museums and places to visit while you are here. Enjoy!