If you have not much time to spend but want to explore … More
If you have not much time to spend but want to explore the most interesting & most exciting stuff in Taiwan, I think you better spend your days in Taipei city only. This trip plan focus more on shopping, night market, taiwan local food & hotspring.
if u got time to spare, try visit the countrysides. Wulai south of Taipei to witness the waterfall 1 hour by LRT and bus from Taipei, or organize a day trip to Chuifen northeast of Taipei to get a specular view of the port of Keelung, the Strait of Taiwan and the East Sea.