Continued...
TAIPEI 101
Currently the tallest building in the world and the number one tourist attraction in the city, this building was designed to resemble a bamboo stalk, with 'ribbons' tied around each segment (as is the custom with potted bamboo). 
Located in the heart of the financial district next to the Taipei World Trade Center and Taipei City Hall, it is easily reached by bus or just a short walk from the MRT. The staff at the Taipei Hostel can provide you with directions, although it is pretty easy to find on its own owing to its size. There is a fancy shopping mall inside as well as an incredible (and rather expensive) food court that offers one of the widest arrays of Chinese food in the world! If you come to Taiwan for the cuisine, Taipei 101 is a must-see regardless of the cost. There is an observation deck at the very top; admission is 350 nt per person. The view is spectacular and dizzying.
TAIPEI ZOO
The Taipei zoo is over a hundred years old and one of the top tourist attractions in the city. Take the MRT directly to the entrance and bypass the traffic. It has spacious enclosures and features hundreds of exhibits. There is a lot to see, so wear a comfortable pair of shoes. There are plenty of food outlets so don't worry about lunch. Try to avoid going on weekends unless you enjoy huge crowds.