If you google “highest peak in Taipei”, you'll find 🏔️ 七星山 Seven Stars Mountain in Yangmingshan National Park. It's a 30-minute bus ride from 🚇 Shilin Station to the trailhead, and it takes me somewhat under an hour to reach the top from there. Qixingshan is a dormant volcano, and at some points, you can still see (and smell) sulphuric gas coming out of the ground. The weather is also unusual and ever-changing as the mountain's thermal activity creates an abundance of mist. My video from the top looks like a time-lapse, that's how fast the clouds are moving. One moment I marvel at the landscape below, no five seconds later (the time it takes to get my camera ready) clouds and fog cover the entire scene. Not to worry, they move on as fast as they have appeared.
This blog has an excellent and more thorough summary of this hike. In particular, take note of the transportation advice:
If completing the entire hike sounds better to you, take it from me, you should hop on the shuttle bus from the Yangmingshan Bus Terminal and take it all the way to the 🚌 Lengshuikeng bus stop.
From there you'll hike to the peak of the mountain and once you're done you can complete your hike by heading down the mountain toward ‘Xiaoyoukeng’.
The reason why I suggest taking this route is because it is considerably easier getting on the bus at 🚌 Xiaoyoukeng than it is at ‘Lengshuikeng’ which often has long lines.
Unfortunately, Yangmingshan is not the closest to where I live in Taipei. Otherwise, this could quickly become a regular weekend (or even weekday morning) hike. I'll still try to come back often and explore other trails in the area and some of the hot springs.