5 days in Taipei
There is something for everyone; hiking trails around the nearby hills give excellent viewpoints over the city, day and night (Elephant Mountain is the best); there are many cultural sites such as the National Palace Museum and Chiang Kai Shek Memorial Hall; night markets are excellent places to go shopping, especially Shilin Night market; there are plenty of night clubs for partying, some offering free flow after paying for entry; and of course Taipei 101 is a must see!
Insider Tip:Tourist travel passes are a good investment, there is the option for 2 day, 3 day, and 5 day. These can be purchased at any MRT station and give you unlimited access to all MRT services and bus services (except 4-number bus services which go outside the city). I bought the 5 day pass for $700twd (it was certainly worth it and removes the hassle of buying tickets and budgeting for transport - unlimited travel around Taipei with the swipe of a card!)