If you want to go for a walk, here is a little video about how you get from Chengchi University to Zhinan Temple and from there further up to the tea house area.
I think Zhinan Temple is quite interesting and you get good views over Taipei from there. It's right beside the gondola station, so getting there is easy. I like to walk in the Maokong area, lots of trails, but I usually avoid the places that tourists usually go, like the tea houses. Perhaps on a weekday in the evening it can be nice, drinking tea and looking down at Taipei.