Will be in Taiwan from 2/16-24/14...Taipei, Taichung, Tainan, Kaohsiung...weather and what to wear.

Would you mind confirm the period?
You mean you want to travel in Feb, from 16 to 24 in 2014?
If so, according to the previous record, the average temperature is around 15 to 20C in Feb for Taipei and Tui Chung and a little bit highin Tainan. It is about 19 to 22C for Kaohsiung.
It is suggested to wear a thin sweater and thick coat.

thank you. yes, february next year.