Kaohsiung and Tainan
Kaohsiung and Tainan, both located in the south, are two of Taiwan's major cities. Tainan was the capital of Taiwan for a long time before Taipei, and has been a major settlement since the 17th century. It's got a lot of history and charm that Taipei lacks, and I recommend it as a place to definitely visit if you come to Taiwan. Kaohsiung is near Tainan, and is Taiwan's second city. It's got some nice sea and river scenery, is more wide open than Taipei and has some splendid subway stations. At the very bottom, there're a few photos of Taichung, the main city in Central Taiwan, and Keelung, a major port city north of Taipei.
