These are some places to visit
1. Modern Toilet Restaurant
2F, No 7,Ln 50,Xining S. Rd., Taipei City (Ximending)
2. Shifen Old Street (十分老街)
Shifen (十分) Sky lantern (天灯)
3. Shifen Waterfall (十分大瀑布)
3. Jiufen Old Street (九份)
4. Taipei 101
Directions: Blue Line to Taipei City Hall Station
5. Raohe Night Market (饒河夜市)
Directions: Green Line to Songshan Station, exit 5
6. Danshui (淡水老街)
Directions: Red line to Tamsui Station, exit turn left and walk along the waterfront
7. Shilin Night Market (士林夜市)
Directions: Red Line to Jiantan Station, exit 1. Diagonally across the street to the left to enter the night market.
9. Taipei Amusement Park
10. Miramar Entertainment Park (Mall)
11. National Palace Museum
12. Kee Lung Miao Kou Night Market
13. Tamsui Old Street Market
14. Taichung Rainbow Village
I've visited a few, not all of them..Taipei 101 is a must...its beautiful at night. Ximending, shilin night market are also nice...
Some in the list might not be exactly in Taipei.
The secret of life is honesty and fair dealing. If you can fake that, you've got it made. - Groucho Marx (1890-1977)