Night Market Near Ximending
While Ximending is opening at night, and is somewhere you buy things, it isn't what we mean by "Night Market" in Taiwan. A Taiwanese night market is a special experience of traditional food and social experience.
Taipei Hwahsi Tourist Night Market is the closest night market, and as the name suggests has facilities for tourists. It takes about 25 minutes to walk, or 10 minutes in taxi. You can use the MRT to go just two stops to the Shandao temple station, but this won't be much faster than walking.
Try also Shilin Night Market which is more a real local night market, but a lot further away in the north of the city. If going by taxi though it is still only 20 minutes, or by MRT subway train it will be 6 stops, with one line change.
Shida Road Night Market – a more recently established but very popular night market. Situated at the northern end of Shida Road just outside Taiwan Normal University it attracts many young people, who are on a budget like university students the world around! So expect cheap, but trendy, shops, stalls and snacks. By MRT it is 4 stops and one line change.
Gongguan Shopping area while not strictly a night market this one is busy at night again with Students, this time from National Taiwan University . This is even more southerly and takes 20 minutes in a taxi. Or 5 stops by MRT with one change.