Taiwan's two major cities, Taipei and Kaohsiung, both have Mass Rapid Transit (MRT) metro systems. They are clean, safe, convenient and reliable. All signs and ticket machines are in English. English signs around stations indicate which exit to take to nearby sights. Posters indicate bus transfer routes.
Check out the stations' websites, which both feature excellent maps of areas around each station.
Kaohsiung MRT (http://www.krtco.com.tw/en/) Two lines, 37 stations, 42.7km of track. Connects with the international and domestic airports. On average trains leave every four to eight minutes.
Taipei MRT (http://english.metro.taipei/) Ten lines, 102 stations and 112.8km of track. New lines in the works. Connects with Taipei (Songshan) Airport, and is expected to connect with Taoyuan International Airport by the end of 2016. On average trains leave every three to eight minutes.
Taichung's MRT is scheduled to open in 2018.