Taiwan, other than being famous of delicious meat, seafood, and tropical fruits, also, I will say Taiwan is a vegetarian-friendly country. Though Taiwan is not on the list of “The 10 best places to visit if you are vegetarian” (The telegraph), you can still find a lot of vegetarian-friendly restaurants while you visit any city or even suburban.
You can ask any Taiwanese like “where can I find su shih restaurant?” you will get a big smile and right direction. However, it (su shih) sounds like Japan famous food sushi, but you just need to show them this picture down bellowed:
Most of those vegetarian-friendly will offer traditional “Chinese fast food” such as fried noodle (Chǎomiàn) or fried rice (Chǎofàn). You can also find some small restaurants offer “su shih buffet” for you to pick up 3~4 different dishes at 2~4 USD per meal.
No matter what food you like and want, you will be satisfied here. All you need to do is just come, visit us, and enjoy this great trip.