I am not a vegetarian. I never plan to become one, with my cultural background (full of meat) it would be hard for me to adopt, or even, I would not really want to be one. But but but this topic is not about me, but about those of you who plan to be in Taiwan and worry about if being a vegetarian will cause some major adjustments.
Well, don't. From what I heard from other expands that travel around Asia and end up one way or another in Taiwan is that Taiwan is ultra vegetarian friendly. No matter if you plan to cook at home, eat outside, hang out and eating with non-vegetarians,or even attend wedding banquet - there is plenty of food around to let you stay full without a touch of meat.
If you eat at home, which is by far the cheapest way to nourish yourself (do not kid yourself, even if you are single - eating and cooking at home is still far cheaper than eating outside local food.) I usually get my groceries in local supermarkets, Carrefour and Welcome, or local wet markets (some are open in mornings, others at nights.) Local markets might not be necessary cheapest - that depends, but they do have freshest fruits and vegetables there directly from farmers.
Eating out? A bit more expensive if you ask me, and it can get quite monotonous if you dine in just specific area. You will find a lot of vegetarian only restaurants almost everywhere, as well as other restaurants offering vegetarian food. In case you do dine in a local restaurant that offer meat, make sure that cooks know you do not want any meat. They often put some pork or meat sauces on the vegetables for a better taste.
If you attend any party or a wedding banquet, announce beforehand that you are vegetarian. It is not a problem at all for the host, because venues are prepared for that and you will be served special menu to accommodate your needs.
As for the average costs, I won't mention it here, because it would be way too broad. However, vegetarian food tends to be more expensive than non-vegetarian food.