Yangmingshan

 

It's called Taipei's backyard.  This mountain range and the nature surrounding it make for endless exploring potential.

BEITOU —The easiest way to get up here is by taking the small #16 bus from Shilin MRT Station.  During the weekdays it should be pretty smooth sailing getting up here.  Weekends are a different story. 

There are a few main peaks and areas that people frequent up here. They are: Qingtiangang Grassland, Juansi Waterfall, Datunshan Lookout, Qixingshan East Peak, and Qixingshan Park. You can google those spots and see which ones seem interesting to you.  

Personally if I was going to visit only one time I'd hike Qixingshan East Peak, but my favorite peak to visit on my scooter is Datunshan Lookout.