(Since this article was written in 2010, the Elephant Mountain Metro Station has opened. The station is obviously a good starting point for trips to Elephant Mountain, and the route from that area is now much more clearly signposted. But because of the easier access, you will find a lot more hikers on that part of the mountain now!)
How to get to Elephant Mountain?
From Taipei 101 it takes about 15 minutes to get to the start of the hiking path.
First, walk east along Xinyi Road for about 10 minutes to the junction of Song Ren Rd and Xinyi Road Section 5.
Keep walking in the same direction across Song Ren Rd and past NY Bagels. After about 30 seconds, you will see a sign pointing right for the hiking trail.