Hi I'm travelling in this Dec around 10 days trip to Taiwan. seek all the advice here

For Taichung, I only have been to National Museum of Natural Science.
I think Taipei is much more interesting. The Maokong Gondola, National Palace Museum, Taipei 101, Yangmingshan Mountain, Ximenting area, the Shilin Night Market. If you want to get close to the nature, the Cingjing Farm is suggested to have a look.