This is not much of a hike. There is a solid concrete path and road that takes you directly from the train station at Shifen to the waterfall. The viewpoints around the waterfall are incredibly crowded and can somewhat disrupt the view. I recommend going early to beat the tourists.
A short hike through the mountains in Taipei that connect to neighbouring mountains. The hike is accessible by public transport and has good views of the Taipei skyline. There are temples along the way and some wildlife can be seen. It's amazing to go straight from city to mountains.