No as a US citizen you don't need a visa to stay or enter in Taiwan Taoyuan Intl. (TPE) airport. Answer is from official Travel.state.gov :
"If you wish to enter Taiwan as a tourist or short-term visitor (less
than 90 days), you do not need a visa. To enter Taiwan, you need:
- No extensions or changes of status are permitted.
- Your U.S. passport must be valid throughout your intended length of stay
- you must have a confirmed return or onward air ticket.
Similarly Visa Policy Of Taiwan and Timatic confirms the same:
National USA (US) /Embarkation Philippines (PH) Transit
Chinese Taipei (TW) /Destination Japan (JP) ALSO CHECK DESTINATION
Chinese Taipei (TW)
VISA NOT REQUIRED.
TWOV (Transit Without Visa):
- Transit hotel is only available for Eva Airways (BR) and China Airlines (CI) passengers. Additional Information:
- Former nationals of China (People's Rep.)
Further as you are traveling on China Airlines, you can also avail Free half day tour as a US citizen. Passengers with 7-24 hour layover before their next connecting flight can participate in this free tour. Details regarding program and policy can be obtained from this website:
Taiwan Free half-day tour