CNNGo thinks Kaohsiung is the third best biking city in Asia, after Kyoto and Beijing, ahead of Jeju and Singapore. I also think it's a splendid place to ride a bike, but for different reasons. The C-Bike system isn't very useful (especially if you're a person of average or larger-than-average Western dimensions) and, as a comment below the article points out, users of the bike trails find themselves crossing major roads fairly often. The climate (reliably dry and sunny, yet not too hot, from October until April) is a massive plus, however.
The final sentence of the Kaohsiung entry suggests the writer didn't do her homework very thoroughly:
If you’re planning a two-to-four day trip from Kaohsiung, we suggest that you ride out toward Taitung City via the scenic South Cross-Island Highway.
The South Cross-Island Highway was mashed by Typhoon Morakot in the summer of 2009 and little has been done to reopen it. You'd have to be a very determined cyclist with a robust set of wheels to make it all the way to Taitung.