Vegetarian in Taipei or places that don't use meat stocks
Going to Taipei with a pescatarian (only eats vegetarian and seafood). Need to find places that don't use any land creatures including in stocks and broths. We'll be staying at the W Hotel but can travel and with be with folks who speak Mandarin.
Makanputra is right. Buddhist restaurants are common throughout Taipei and many non-Buddhist restaurants will have a few clearly labeled (in Chinese, at least) vegetarian dishes.
For a casual lunch, a decent choice is Minder Vegetarian (明德素食園), a buffet style restaurant found in many of the more upscale mall food courts in Taipei. For locations near the W, there's one in the Xinyi Eslite food court and one in Shin Kong Mitsukoshi A8 food court.
Most night markets will have at least one Buddhist vegetarian stall serving various things, including vegetarian stinky tofu.
If you're looking for more upscale (i.e. not in a food court or night market) vegetarian, I can't really help you, but I'm sure there are places out there.
Of course, since the friend eats seafood as well, there is a lot of good sushi in Taipei, as well as excellent seafood prepared in various Chinese and Taiwanese styles. Your friend should have no problem with the latter as long as you confirm that no four legged creatures were used in any stocks or broths.
In short, your friend will have no problem finding things to eat, especially if you have a Mandarin speaker with you.
Many restaurants carry something vegetarian. Keep in mind that strict buddhist vegetarian also bans things like hot chilies, garlic and onions. Pescatarian, I think, is relatively rare, compared to the Buddhist vegetarian, so that will take a bit of explaining. But restaurant owners understand the whole vegetarian concept, which makes it relatively easy.
Buddhist buffets are pretty common - small restaurants that have a buffet of vegan items, sold by weight, or by the owner eyeballing how much you've got on your plate.
For specific restaurants, I've been to a more upscale vegetarian buffet place near Daan Park, (http://www.springfood.com.tw/) that we take vegetarian visitors at work to. 600 NT for dinner, has salads, soups, hot and cold buffet, dumplings, made to order noodle station, desserts, non-alcoholic beverages, etc. The food is very good, although I don't recommend the vegetarian sashimi as anything other than a novelty.
Found some vegetarian restaurants online, but you probably want to ask around or do more research before going.
Antrodia Themed Restaurant
功德林 (Shanghainese vegetarian, they have vegetarian soup dumplings
There are many seafood themed restaurants around Taipei (where you can clearly see live fish tanks, fish on ice on display) that will also fit the bill nicely. For those places, you ask the price, point to what you like, and tell them how you like them prepared...some options include sashimi.
Here's an example of one at Ningxia Road Night Market: http://0225501259.tw.tranews.com/.
These types of places will offer a variety of stir fry, and you can specify no meat or ask for recommendations (and/or check the menu and ask to make sure no meat).