A large number of taxis are available in most major cities. Basically, taxi fares in all major cities are set by the local city government itself, and there are few variations. The meter may not be used for out-of-town or long-distance travel; travelers are advised to confirm thecharging method before getting in a taxi.
For more information, please see Taiwan Taoyuan International Airport - Taxi, Kaohsiung International Airport - Taxi.
Most drivers do not speak English, so it is a good idea to have hotel personnel write both your destination and your hotel's name and address in Chinese, along with the projected cost of each one-way trip for you.