The regions of Taiwan are based on the historical administrative divisions. However, most of the definitions are controversial.
Eastern and Western Taiwan: the Central Mountain Range separates Taiwan into east and west.
Eastern Taiwan: Yilan, Hualien and Taitung.
Western Taiwan: other divisions from Taipei to Pingtung.
Northern and Southern Taiwan: Zhuoshui River, the longest river of Taiwan, flows through about the middle of the island.
Northern Taiwan: Taipei, New Taipei, Keelung, Taoyuan, Hsinchu (City/County), Miaoli, Taichung, Changhua, Nantou.
Southern Taiwan: Yunlin, Chiayi (City/County), Tainan, Kaohsiung, Pingtung.
Regions of Taiwan Wikipedia
The most widely used definition is from the Council for Economic Planning and Development, Executive Yuan. The quadchotomy scheme corresponds to the prefectures under Qing Dynasty rule.
The hexchotomy scheme corresponds to the prefectures under Japanese rule.