Taipei is the capital city of Taiwan and it is a bustling metropolis with interesting things to do and places to see whether you are there for a quick 1-day stopover, or if you have a week to spend.
If you enjoy visiting museums, then the National Palace museum is a must see. It contains in its permanent collection, the largest collection of Chinese historical artifacts.
Taipei also has a diverse food scene. You can try traditional dishes such as Xiao long bao (from Ding Tai Fun) or Stinky Tofu in the night markets to high-end restaurants and international cuisines.
If you want to explore the out doors, Taipei provides interesting sites such as Yaoming mountain, with beautiful Azalea blooms in March/April that cover the mountain. Or if you are there in winter, join the locals and soak up the warmth in the hot springs.