I've been to TPE quite a bit (and lived there) so I can confirm there will be always at least one currency exchange open. They all have pretty competitive rates, actually better than you can get in the city at most places. (and if you want to change something other than USD, CNY or perhaps EUR, TPE is the place to do it) ATMs are obviously a good option but many of them outside the airport don't accept foreign cards so beware. (My Standard Chartered HK ATM card is rejected by most Standard Chartered ATMs in Taiwan... and sometimes they even debit my account without giving me cash)