basically a place that can make one forget about the city and enjoy nature.
Take Bus 260 to Yangming Shan from Shilin MRT station exit 1
Take Kamalan bus from Technology Building MRT to Yilan where you’ll find lots of nature.
It’s not 100% forgetting nature but I enjoyed doing this in the hot summer days:
Take MRT to Neihu station, walk up jinhu rd, then hike along 白鷺鷥山步道西登山口 and cross to the other side to dahu park. Then you can take a refreshing swim at the public swimming pool at the park.
Also Teapot mountain is about 1 hour bus ride
The MRT gives you access to numerous hiking trails in and around Taipei. If you combine the MRT with buses, you’ll get even more options. I used to think Guanyinshan, the lone mountain in Bali, is out of reach of public transport. Someone later showed me the buses you could take from Luzhou MRT to get to the trailhead. Easy peasy.