Two options at day, 1. Yangmingshan National Park - small oil pit. 2. Beitao - hot spring valley and Beitou Hot Spring Museum, Beitao part, and probably explore public hot spring. Plus Shilin Night Market at night.
Special geographic scenary tour in Taipei at day. Delicacy and children play at night. Hotstar big big chicken pie，Red bean green tea ice etc.Special suggestion: pig brain soup. Maybe a visit to Aunt Ivy's place.