Taipei is internationally renowned for its night markets. Some of the country's best food can be enjoyed on the streets, and greater Taipei alone has more than 30 major night markets and countless smaller ones. In fact, in the first ever Michelin Guide to Taipei (2018), 10 of the Bib Gourmand selections were night market vendors!
Obviously, visiting a night market is a must when you come to Taipei, but how can you choose which one when there are so many? Most tourists go for one of the five most famous ones, starting with the largest, Shilin Night Market. Raohe, Ningxia, Tonghua, and Huaxi night markets are other very popular choices. To be fair, all of these night markets are literally overflowing with amazing foods, and many locals frequent them as well. 8 of the 10 Michelin-listed food stalls are at these top-5 night markets.
Still, if you truly want to "go local", then get off the well-trodden tourist path by visiting one of Taipei's less famous night markets. My top recommendation would be Nanjichang Night Market, located in the city center (Zhong Zheng district). The night market is small but packs in a high concentration of extremely delicious foods. It's popular among locals, yet it remains rare to see a foreign face among the crowds. It's also the only lesser known night market to get a Michelin listing (2 of them, in fact): one for a stinky tofu joint and another for sesame oil chicken.
Two other Taipei City night markets that are off most tourists' radar are Liaoning and Jingmei night markets. If you venture into New Taipei City (still accessible using the Taipei MRT), then other non-touristy night market options include Sanhe Night Market in Sanchong, Xinzhuang Temple Street in Xinzhuang, Nanya Night Market in Banqiao, and Le Hua Night Market in Yonghe.