One of the best places to see a good view of Taipei overall, with a view of the tallest building in Taiwan is at Elephant Mountain. 

You can easily get to this area by taking the last stop on the red line towards Elephant Mountain.

Upon exiting, follow marked signs that tell you to walk through a small park, and up a hill to reach the trailhead of the hike.

Note that bring a bottle of water, especially in sunny and hot summer days as when I hiked up those steps .. I was sweating SO MUCH! And almost passed out at the top.

But as you can see from my photo summary below, the top of Elephant Mountain gives great views of Taipei:

Have you been to Taipei?