There is only one oridinary express train from Taitung-hsin TO Hua-lien , in the morning 6:48 .
after school children get off , the whole coach is mine .
The mountain won't be disappeared in Taitung .
I suggest you to drive from Hualien to Taitung along Highway no. 11 (Hua-Tung Coastal Highway) to enjoy the beautiful scenery of Pacific Ocean and drive back from Taitung to Hualien along Highway no. 9 (Hua-Tung Valley Highway) for the mountain views and many attractions in this page.
We were taking the airplane back to Taipei. It took about 1 hour's flight. The pre-saled discount ticket is about NTD 1,400 (USD 40)one way. We bought the tickets from http://www.ezfly.com but that is a web site in Chinese.
There are also the flight between Taichung and Taitung.
We take the express "Hot Spring Pricess" from Hualien to Taitung. It departs from Taipei at 7:10, Hualien at 10:30 and arrives Taitung at 13:30 daily. The ticket is only available from the travel agents. The seat of this tourist express is bigger than that of the ordinary trains in Taiwan. They also provide you the breakfast and the lunch on the train.