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You can take a train to eastern Taiwan, on the way enjoying the scenery along the North Link Railway and the Hualien-Taitung line and, when mealtime comes around, savoring the famous Chishang box lunch. After arriving in Taitung you can visit Xiaoyeliu, Water Flowing Upward, Chulu Farm, and other sights, finally returning to Zhiben to relax and loosen up your bones in the hot-spring baths there.
On the second day you can catch a train on the South Link Railway from Taitung to Fangliao in Pingtung County on the west coast. This is the only railway line that allows you to enjoy both the Pacific Ocean and the Taiwan Straits, starting out along the lovely Pacific and cutting through the southern tip of the Central Mountain Range to the west coast, where the beauties of mountains and seas as well as the fascinations of aborigine culture await your eyes.
Since you are in southern Taiwan, you must not miss the opportunity to visit Kenting National Park. The park is situated on the Hengchun Peninsula and has an abundance of oceanic resources, a splendidly mysterious undersea world, and vast and unique coastal topography including coral cliffs on the west coast, wind-eroded landscapes on the east coast, and the limestone terraces and collapsed landscapes on the south coast. Jialeshui, Windblown Sands, Longpan Park, Eluanbi Park, Guanshan, Sheding Nature Park, and Maobitou are all outstanding places for viewing natural scenery. If you want to experience the atmosphere and garden arts of southern Fujian Province, you can go to the Kenting Youth Activity Center to see the four-sided courtyard houses there and take some photos amid these traditional Chinese surroundings.