Orchid Island 蘭嶼
A far-outlying, extraordinary island between Kenting and Taitung.
If you're planning to visit Orchid Island 蘭嶼 (Lányǔ) during your Round-the-Island loop, try to get a spot on the 3-hour ferry from Kenting (more specifically, from Houbihu Harbor 後壁湖) and add a few unique days to your trip by visiting this far-outlying aboriginal island. Skip the Kenting-Daren-Taitung/Dulan sections by hopping on a ferry back to Taitung. Alternatively you can take a (shorter/more available) return trip from the Fugang Wharf in Taitung.
This extraordinary island is so remote that you should be 100% sure there are absolutely no strong winds or typhoons coming in the next few days: sea and air services are cut off, sometimes with just 24 hours' notice.
Refer to your usual sources for things to do locally. Suggestions are welcome.