Many people go to Taiwan for a variety of inexpensive good food. There are restaurants every where: street food, night market, and all kinds of restaurants, coffee shops and tea houses. However, when it comes to Taiwanese cuisine, non-touristy authentic restaurants are limited.

Here's one recommended by a local Taiwanese, a small restaurant with no English name. I think that the owner's last name is "Zhao" and the translation is "Zhao opportunities" in English, phonetically the same as "Finding opportunities".  The restaurant environment is very local but the food is good! It is definitely popular among the locals.

Address: 1F and 1B, No. 83 Tong An Street, Daan District, Taipei (near Hunghua Night Market)
Tel: 2733 7334(1F) 2732 2330(1B)

Booking is recommended because it's always full. Closed on Sundays.