I also am going to Taipei, and have done a little research, especially on the "local" options. Perhaps if I post what I found, some locals or other frequenters of Taipei might be encouraged to post as well.
First, I recommend the following blog: http://hungryintaipei.blogspot.com/. She is very descriptive, so you can probably figure out what you might or might not like of her recommendations.
Here are some places I think seem good (by description only, since I have yet to visit):
Hunanese: Peng Yuan – 2F, 380 Linsen N. Rd.
Dim Sum: Chao Ping Ji at San Want Hotel, 2 FL - No. 172, Zhong Xiao East Rd., Sec. 4
Chinese Breakfast: Yong He Dou Jiang Da Wang (or Yong He Soy Milk King) - 102 Fuxing South Road, Sec. 2
Sichuan: Xiao Shen Ji - No. 45, MingShen E. Road, Sec 4, 2 FL (SongShan District)
Shanghaiese/Xiao Long Bao: Kao Chi - 5 Yongkang Street
Finally, for a splurge (and if you're not put off by eating non-Chinese food in Taiwan), I have heard the branch of L'Atelier de Joel Robluchon in Taipei is really good.