Night markets are a very enjoyable experience for a tourist and a part of everyday life for the Taiwanese. You can get everything here: great food, cheap clothing, trinkets, souvenirs, electronics, etc. They usually open around dusk and close up shop at around midnight. Don’t be surprised if you see stalls with no vendor around (usually with music CD’s or DVD’s). Some of the vendors operate illegally, and quickly disappear when cops show up.
Hwahsi Jie a.k.a. Hwahsi Tourist Night Market or as it is affectionately known as Snake Alley is a good bet for starters. You can dine on barbequed rattlesnake here, have turtle soup or munch on a stir-fried mouse (or two). Funny enough, this type of food will most likely nauseate your Taiwanese friends, and if you dare to eat it, they’ll look at you like the alien that you are. It seems that most of the stalls offering these "exotic" foods are for the benefit of the tourists. Keep in mind, that if you really want to try "authentic" Taiwanese food, you should concentrate on the street vendors selling a variety of steamed buns or dumplings floating in broth. If you’re feeling VERY adventurous, you can order a set of alcoholic drinks in any snake restaurant which are various snake fluids like blood, bile or sperm (yes… you’ve read it right) mixed with a local liquor called gao liang. As unappetizing as it sounds, I’m sure the snake additives only improve the flavour of the liquor (which by itself has a flavour reminiscent of kerosene or bug repellant).
Nonetheless, Snake Alley is great place to load up on souvenirs, music and videos and a variety of other trinkets. It once used to be notorious for prostitution, but in the last few years Taiwan’s government cracked down and cleaned up the place. To access Snake Alley take the metro to the Lungshan Temple station.
There are plenty of other night markets to be found in Taipei. Location information can be found on Taipei City Government’s homepage at
http://www.dot.taipei.gov.tw/travel/english/info/info2/food10.html.