I know nothing about these sites' accuracy, but these below were the
best I found with "https://DuckDuckGo.com" and "site:gov.tw" term.
* The Bank of Taiwan buys American Dollars (USD) at 30.08 NTD, and sells
them at 30.77. They take payments to the government as well as handling
currancy exchanges in the airport. Here is their list of current
exchange rates for many currancies: https://rate.bot.com.tw/xrt?Lang=en-US
* This site says to expect roughly 2.5% service fees for currancy
exchanges.
https://www.ihatetaxis.com/convert?amount=100&from=TWD&to=USD&destination=TPE-Taipei-Taoyuan-Airport.
It also has lots of helpful information on ground transporation to and
from TPE in English.
* Official web page of the TPE airport services includes showers!!! and
banking, ATM etc. information with locations in many (all?) terminals:
http://www.taoyuan-airport.com/english/store3
* Locations and 24hr phone numbers of exchanges at the Taoyuan Airport
(TPE)
http://airportbanking.com/taiwan-taoyuan-international-airport-tpe/#currency-exchange.