Yoz....I will be there from Jan 5th. Maybe we can meet up. Here's a list of what you can take.
Taipei City:
-Hua Xi Street: snake alley, have fun eating the snakes there, don't allow pics for their show tho.
-Taipei 101: latest skyscraper, one of the tallest in the world.
-Shi Lin Nite Market: Great place for shopping and makan. A nite life hub
-Xi Men Ding: Hip place for shopping, you will see a lot of school kids there and the latest hip hop fashion here. Some girls might be willing to let you take their pic if you look pro enuff. Might see some idols there too.
-Chiang Kai Shek Mem Hall: Huge monument in the midst of the city.
-Taipei Main station. asiaworld(largest mall in asia), there's also lost of temples and monuments you can go to too....
-Warner Village: The area around it is quite nice.
- Lai Lai Hotel: One of the best hotels in Taipei, the building design is based on the old chinese architecture. This is the one that Myst is recommending.
- NTU: National Taiwan University; worth taking a look, the main plaza and walkway is very nostalgic, you will never see classrooms like this in Singapore.
Around Taipei:
- Tan Shui: Nice scenic spot, avoid weekends tho, very packed.
- Yang Ming Shan: Commerical Tourist spot
- North of Taipei; Keelung: 40+ mins drive, nice harbour view, fantastic at the evenings.
There's still a lot that i can recommend, but these are the main ones. I had spent a week there and I still think I miss out on a lot.