I would recommend checking other threads on FT or tourist websites as what you will want to focus on is largely up to personal preference. I am a bit spoiled in terms of experiencing Taipei since I visit quite frequently, and two days is not a lot of time! In terms of tourist activities that are most distinctive, I would recommend the National Palace Museum, Taipei 101, and a sampling of Taiwan's many night markets. The choice of night markets will again depend on personal preference as they widely vary in size as well as tourist crowdedness.

Other possibilities include the CKS and Sun-Yat Sen memorial halls and the Taipei Botanical Garden. I am also a fan of Dongmen market for both food and shopping. The Taipei Zoo is also excellent (and very inexpensive) but probably a lower priority with your time constraints.