Go camping in Neiwan:
Go camping and hot springing in Taian (or just hot springing in Cingquan (on the 112 road down to Guanwu.
Hike the Syakaro Historic Trail:
taipeitimes.com/News/taiwan/ … 2003101473
There probably isn’t that much to do in Zhudong itself but you are well situated to take advantage of Taiwan’s mountainous beauty.
Start exploring your area on scooter. There are endless roads and trails and stunning vistas, waterfalls, hot springs, cold springs and swimming holes that can be yours alone.