To Bassman’s list I would add the Folk Arts Museum. It is a little pricey to get in but I feel it’s worth it. The displays are well organised and they sometimes have special activities going on. There is a house set up as a middle-class house from - I don’t remember what dynasty - but anyway it’s interesting.
The two ‘must-see’ temples are Tianhougong, dedicated to the daoist deity Mazu (which has an interesting exhibition at the back), and Longshansi, dedicated to the buddha Guanyin. Unfortunately last time I went they were doing some work on the Longshansi so it was not possible to see all of it, but hopefully that’s finished by now.
Other local specialities are ‘dragon whiskers’ candies, cow tongue and ox eye cookies (named so because that’s their shape, not what they’re made from!), a kind of sweet/salty sponge cake with fried onion crumbs on top, and of savory dishes; ‘shrimp monkeys’ (fried shrimp you eat whole; as you see the shrimp crawling about in big basins before they’re taken out and fried, I don’t have the heart to eat them).
There is more than one bus that goes from Taichung city; I think one goes from the Gancheng bus station on Shuangshi Road. Private message me if you need more info.