If you are traveling in Taiwan, dont limit yourself to exploring what you see overground because they got a ton of goodies underground too! The area around Taipei Station has a huge underground shopping mall called Taiwan City Mall. One of the sections is absolutely filled to the brim with Japanese pop culture - anime and otaku goodness.
If you are heading there, get out the station at exit Y17. The address would be 台北市市民大道一段100號