What is the best way to get to Kenting from Taitung? Take the train from Taitung to Pintung, and then take a bus? Thanks in advance! 
You can get off before Pingtung in Fangliao and then take a bus. The best way though is to rent a scooter, ride to the top of the Nanhui gonglu and then head south on the tiny road that runs runs through Mudan. A very special corner of Taiwan.