The best choice after the Shilin night market is Yuan Shan Bowling Court Yuan if you have still energies to spend.
Shan Bowling Court has 36 fairways and opened in the 1966 when it quickly became one of the most popular bowling alley in Taipei.
You can play air hockey after you enjoyed bowling and it's quite cheap too.
No. 6, Section 5, Zhongshan North Road, Shilin District, Taipei City, Taiwan 111