The former tallest building of the world (until the Burj Khalifa in Dubai was built), Taipei 101, has probably the most spectacular views of the city. The observation deck at 382 meters above the ground not only offers great views, but there is also a bar where you can get a drink and audio tours in various languages. The tower itself consists of 101 floors (hence the name) and has a total height of 449 meters. It’s designed to resist heavy earthquakes and typhoons by using a massive steel pendulum (damper), which is the largest in the world and can be seen at the observation deck. For more information visit the tower's official website: http://www.taipei-101.com.tw/en/index.aspx
National Palace Museum
If Chinese art is what you like, then you should definitely make a visit to Taipei's National Palace Museum. The museum is the home of one of the largest collections of Chinese art, including paintings, statues, religious objects and calligraphy. Furthermore it is also possible to visit the museum gardens with lots of ponds, waterworks, pavilions, all built in a Chinese architectural style. http://www.npm.gov.tw/en/
Yangmingshan National Park
Just outside Taipei you’ll find the Yangmingshan National Park. The park, which features forests, mountains (up to 1120 meters in altitude), grasslands, flower fields and hot springs covers about 115 square kilometres. The park can easily reached by bus and the best time to visit is early spring. More information can be found on http://english.ymsnp.gov.tw/.
Confucius and Longshan Temples
The Confucius Temple was built in the 1920's and is a good example of Minnan style architecture. The Longshan Temple was founded in 1738 and has been rebuilt several times. This impressive temple used to be a centre of self-defence as well. For more information on the temple, visit http://www.ct.taipei.gov.tw/ for the Confucius Temple and http://www.lungshan.org.tw/ for the Longshan Temple.
Chiang Kai-shek Memorial Hall
Probably one of the most visited attractions in Taipei is the Chiang Kai-shek Memorial Hall. Spread over a surface of 250,000 square meters, the hall is accompanied by the National Theatre and National Concert Hall and a beautiful garden. More information: http://www.cksmh.gov.tw/eng/