Day 1–2 in Taipei (night markets, Beitou hot springs, day trip to Jiufen), Day 3 train to Hualien and explore Taroko Gorge, Day 4 bus or train to Sun Moon Lake via Puli, Day 5 return to Taipei via the high-speed rail. A 3-day Taiwan High Speed Rail pass pays for itself if you do this loop.
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