Taipei is an awesome city and a beautiful small country.  The temples alone make this an unbelievable place to visit.  The Confucius and Lung Shang Temples are beautiful places to see.  You MUST visit the National Theater and Concert Hall, it is a place that my words can not do it justice.  It is this huge, immaculate and peaceful place that makes you lose track of time.  Another good place is the Chiang Kai-shek Memorial Hall.  Two great hotels in Taipei are the Asian World and the Ritz Landis.  The Grand hotel is another marvelous hotel which is close to the National Palace Museum and the Yangmingshan National Park.