Danshui and Bali on the Taiwan Strait
While the night markets in Taiwan a packed with food providing instant gratification, the morning market in Danshui is for people who prepare their own food. The closest thing I've ever seen to this in the US is the Pike Place Market in Seattle, but even that doesn't come close to providing the kinds of meat and it certainly lacks live animals. You have to be an early riser to catch the Danshui morning market, which requires a ride on the MRT subway system to the end of the line. Once you're there, you can browse fish mongers, see pigs being butchered, buy a live chicken to take home for dinner, or simply stock up on vegetables.
While you're in Danshui, there's also a boardwalk along the mouth of the Danshui river and the Danshui Fisherman's Wharf, which is a tourist site aimed more at local Taiwanese looking to escape the city than traveler's like me. Small passenger ferries provide transport from the boardwalk in Danshui out to the Wharf, which is highly recommended over walking. Even seeing someone washing their pig on the side of the road didn't quite make up for the length of the walk. Danshui also has a Maritime Museum which covers a great deal of the history of ships in the port town including an aboriginal canoe on display.
You can also take the ferry across the river to Bali, which has another boardwalk area and the Shihsanheng Museum of Archeology.