The travel problem this week is not a lack of places. It is that every household with a car had the same four days off.
Highway authorities expect Friday southbound traffic at about 1.5 times a weekday, with Freeway 5 toward Yilan closer to 1.8. High-occupancy controls hit the southbound on-ramps of National Freeways 1 and 3 out of Taipei on Friday morning, then the northbound Yilan ramps of Freeway 5 from Saturday to Monday, 1 p.m. to 6 p.m. Night tolls drop to zero from midnight to 5 a.m.; that only moves the queue.
Qingjing, Hehuanshan and Sun Moon Lake are the inland magnets. Highway Bureau advice for Cingjing is arrive before 10 a.m. for a day trip or after 3 p.m. if you have a room. Sun Moon Lake: before 11 a.m. or after 4 p.m. The 14 Jia and the lakeside 21 / 21 Jia clog at midday. Parking at 3,000 meters is finite. So is warmth after sunset.
High Speed Rail is running 1,150 trains from 24 to 29 September, 176 of them extras, with more northbound than southbound because the return crush is larger. Tickets sold through the T-EX app, convenience stores and station counters. Unreserved carriages do not guarantee a place to stand near a door. TRA added about 160 holiday trains; the English timetable is on railway.gov.tw.
Domestic flights and the offshore boats also added seats. Kinmen and Penghu fill first. If you do not already have a cabin or a boarding pass, pick a city walk.
A workable trip from Taipei is a reserved THSR seat to Taichung or Tainan on Saturday morning and a return on an early Monday train, not a self-drive over the Central Cross-Island. The Tourism Administration listings at taiwan.net.tw still help for museum hours in those cities. The mountain roads will be there in October.