Part of the set of Four Beasts, four peaks on the outskirts of Taipei city which make up the Nangang District Hiking Trail, Elephant Mountain (象山), is definitely one of the best (and subsequently most popular) places to get a view out over Taipei 101, and parts of Taipei City.
The walk up to the first viewing point (a set of big boulders) is a steep climb, up a paved stairway. From there, the trail continues on at a much flatter gradient. Going further will take you a couple of other viewing areas – which are normally fairly crowded – though there are spots along the way which you also stop at & get a good view through the trees.
There’s plenty of material on the internet on climbing Elephant Mountain, so a quick Google search should help you. The most accessible starting point for the climb is from Lane 150, Section 5, Xinyi Rd. The climb to the boulders takes about 20minutes. I’ve read the entire Four Beasts trail takes 2~3hours to complete, but I’m yet to try it.
The next time, I plan to head up to Elephant Mountain for sunrise (if I can get myself out of bed in time)…