This 2012 article from CNNGo describes 45 easy-to-find Taiwanese foods, all of which are delectable if done well, and gives suggestions where visitors can enjoy them. (Most are in Taipei).
The Chinese script for each dish makes the article especially useful - no need to decipher Chinese-language menus or attempt to speak Mandarin - and people eager to try mainstream Taiwanese fare would do well to print out the article.
My favourites are nos. 6 and 14. No. 11 is often known by its Japanese name, tempura.
Food Culture in Taiwan has some useful background information about Taiwanese seafood, night market snacks and aboriginal cuisine.