If there was only one hike I would have to recommend while you are in Taipei, it would be the Teapot 茶壺山-Banping mountain 半平山 close to Jiufen. The actual hike, which is about 11km, is not challenging but fun with some rock/rope climbing parts. Because the views of Northeast coast from the top are stunning, going there on a clear day is definitely a must. In the morning, we had a sunny weather but once we reached the Teapot peak, we could see a wave of white clouds erasing the whole landscape views and from this point to Banping 半平山, it was so cloudy that we could not see anything!
How to get there
You can reach Teapot Mountain 茶壺山 by train or bus. I personally chose the bus option. Bus #1062 from Zhongxiao Fuxing subway station - exit 1. Once you get out from the subway, do a U-turn and then turn left. The bus stop will be there. You can get off at the final stop, JinguaShi 金瓜石 - The best seats are on the left side of the bus for the view during the way.
Once arrived, enter the Jinguashi park and then, you can ask the direction for the teapot hike at the information center. There are also lots of signs so it is hard to miss this trail.
At the teapot peak, you can either go back or continue to go to Banping Mountain 半平山 - which we did and it's definitely worth it.
After BanPing mountain 半平山, you go down and have a few options including going back to Jinguashi bus station, exploring another mountain or continuing a easy street going down that leads you to Jiufen old street. Last bus leaving Jinguashi to Taipei is at 9.30pm. Easy cards can be used for the whole trip.
Count 1h from ZhongXiao Fuxing station to JinguaShi final stop. The actual hike lasted for about 4h with a quick lunch stop on Banping Mt. 半平山.The best is to go there early morning and if you don't feel too tired, you can take the opportunity to explore Jiufen Village later on.