By road
By road
The mountains are covered in a network of roads, and there are several mini-buses that leave from Zhongzheng Road directly in front of exit 1 at Shilin MRT Station that traverse the mountains.
Public transport information is available online (http://www.ymsnp.gov.tw/H...)
For just NT$60, you can take the 108 bus around the park an unlimited amount of times during its operating hours 0700 - 1730. There are plenty of stops at various locations around the park, but you may have to wait 15 or 20 minutes between buses, so plan accordingly.