Posted 30 May 2012 - 04:03 PM
Not sure if this is the thread that Kouign Aman mentioned, but thought I'd mention a few places in here.
As far as night markets go, Shilin is probably the most famous. In addition to stinky tofu and ô-á-chian (oyster omelette) and the other standards, the white kugua shake (bai kugua zhi) is really great here if it's in season. The fruit stands on the streets surrounding the market are also really memorable - highly recommended.
In addition to Chinese food, Taiwan is great for sushi. I'm vegetarian, but my wife ate at a place in Taipei that, while not cheap, was light years ahead of what you'd get in the US for the same kind of money. I don't know if the place is still open, but it's called Kitcho Sushi (吉兆割烹壽司) and it’s at 忠孝東路四段181巷48號 (#48, Lane 181, Section 4, Zhong-xiao East Road), Da-an District). That area has a lot of other hip Japanese businesses, so I'm assuming there might be other good sushi places in the area. I would guess that for omakase with some kind of drink you'd be looking at $100/US/person, give or take (and the chef refused to accept a tip).
I would really recommend visiting Wistaria House - not only a beautiful environment, but one of the rare "tea houses", even in Asia, where you can actually drink some excellent teas. Also, while maybe not a destination for food in and of itself, the food there is quite good.
For Chinese style breakfast, I've found that it's not like Shanghai, where there are pretty good hole in the wall breakfast places all over the place. Street carts are decent for fantuan (rice roll) and sweet soy milk, but for fancier breakfast fare (sweet or salty soy milk or soft tofu / dou hua), Yonghe Doujiang is justifiably the most famous. They have a lot of locations.