A large number of taxis is available in most major cities. Basically, taxi fares in all major cities are set by the city government itself, but the discrepancy among them is little. Out-of-town or long-distance travels may not apply to meter charge in some cities; travelers are suggested to confirm charging method before getting on 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.
English Taxi Association: +886-2-2799-7997