Taipei is one of the great food cities of Asia, and probably the single best place to eat Chinese food outside the mainland. The Kuomintang retreat of 1949 brought cooks from every province of China to the island along with the refugees, and the result is that the regional cuisines of Sichuan, Hunan, Shandong, Jiangsu, Fujian and Cantonese cooking can all be found here in excellent form, alongside the distinctive local Taiwanese cuisine that has developed over four centuries of Hokkien, indigenous, Japanese, and mainland influence.
The essential Taipei experience is the night market. Start with Shilin (the most famous, most touristy, and still worth it once), Raohe Street (a more compact and manageable option near Songshan station), and Ningxia (the most local in feel). Look for oyster omelette, beef noodle soup (Taiwan's unofficial national dish), stinky tofu, xiaolongbao dumplings (the famous Din Tai Fung chain began as a single Taipei noodle stall), oyster vermicelli, pepper buns, scallion pancakes, and the obligatory bubble tea — which was invented in Taiwan in the 1980s. Beyond the markets, Taipei has an extraordinary number of specialist restaurants at every level; the district around Yongkang Street is famous for refined regional Chinese; Da'an has the best café culture and the newer wave of modern Taiwanese cooking; and the Eastern District around Zhongxiao East Road is the trendy dining strip.