You can ride around the island on a scooter in about 30 minutes, but give yourself at least a day. This island was made for exploring.
The main attractions are the iconic Vase Rock, a giant eroded coral with a thin base and large head, and the slightly underwhelming Black Dwarf Cave and Beauty Cave. Some sites require an entrance ticket; one ticket for NT$120 is good for all of them.
You can also check out the narrow, twisting, root-strangled coral passageways at Shanzhu Ditch (山豬溝; Mountain Pig Ditch; Shānzhū Gōu) and Lingshan Temple (靈山寺; Língshān Sì), just up from the pier. The temple offers fine, clear views across the Taiwan Strait.
For off-the-beaten-path scenery, head to the southeastern coast, where wind and waves have created fantastic rock sculptures.
The enormous Sanlong Temple (三隆宮; Sānlónggōng) is the site of the island's Wang Yeh Boat Burning Festival, which takes place every three years in the autumn, a couple of weeks after Donggang's Donglong Temple holds its festival.