If you want to make an good excursion near Taipei 101, i can advice you to go to elephant moutain near the Tower. From this place you can make different trekkings. The basic trekking is to go to observatory where you can find the tower and all the city. It is a good place at this end of the day but also everytime. I went there during the day and it was very hot in August. Fortunately there are many places to stop and just to enjoy the place. Very good excursion just close the city center.
For a better view of Taipei City, hike to the top of Elephant Mountain. This is a very nice place and especially easily accessible from the center of Taipei. Also known as the Nangang and Xiangshan District Walking Trail, the trail is located near the Xinyi and Taipei 101 shopping district. You can go there at any time of day, but you can give a special mention for the view at sunset. The night view with all the illuminations is also breathtaking. The hike lasts about 30 minutes and includes many stairs. However the hike does not stop there, which means that from there there are many circuits to walk that can then take a good time. If you just want to stop for the city view the tour will be fast enough. If you go further it will take half a day.