the most famous Temple in Taipei, Mengjia Longshan Temple was built in 1738 by settlers from Fujian. It is seen as an emblematic example of Taiwanese classical architecture. I published many picture of this temple on an other article :
https://traveljournalist.com/mengjia-longshan-buddhist-temple-taipei-taiwan-dusk-twilight/
The subway is clean and very convenient , they created many new lines these past years to cover most of downtown.
you can enjoy a concert during a transfer
the National Chiang Kai Shek Memorial Hall
Taiwan National Day 2015 Military Parade rehearsal Chiang Kai Shek Memorial