Japan had Taiwan under its rule from 1895 until 1945. Despite the history of colonial rule, Taiwanese today have largely favorable views of the Japanese. Japan is the third most popular destination for the Taiwanese, after South Korea and China.
Taiwan is also a popular tourist destination for the Japanese, perhaps due to their curiosity of the island that was once part of Japan. The Ciaotou Sugar Factory, the first modern factory in Taiwan, is now a stop on the tourist path. It was built during the Japanese rule and heralded an industrial age as the Japanese went on to construct highways, railways, hospitals and schools. Japan developed hot spring towns such as Beitou, outside of Taipei, where you can still check in to Japanese-style accommodation with futon. You can shop at Uniqlo, the Muji Store, or the Sogo and Mitukoshi department stores. You can eat at Yoshinoya, Mister Donut or at any of the ubiquitous Japanese street-side restaurants. You'll even get complimentary packets of green tea in your hotel room.
After having spent some time in Taiwan recently, I think there are a few things the Japanese could learn from modern Taiwan too. Here is how Taiwan is saving the world: