Below are the potential excursion options for Wednesday afternoon (not part of the official program):
1) Hiking from Nangang to Taipei101.
There is a nice trail starting a few bus stops from Academia Sinica that ends in the city center at the famous Elephant Mountain close to Taipei 101. The total trail is a bit more than 7km and the total ascent is around 550m. So it is a good workout doable within 4 hours during the afternoon. Here is a link describing the trail.
At your own risk.
2) Guided tour for the Museum of the Institute of History and Philology.
The museum inside the AS Institute of History and Philology houses one of the world’s most important collections of ancient Chinese artifacts. Its exhibits feature oracle bones, bronze vessels, and early manuscripts, offering insight into early Chinese writing, ritual practices, and the development of civilization. The museum is closely tied to academic research and presents materials that are often unavailable to the general public elsewhere.
A guided tour from 2-3pm has been arranged; Sign-ups at the registration desk on Monday is required for head-counts.
Other popular options inside or nearby Taipei city that can be reached by Metro includes e.g.,