Three weeks in Taiwan is the perfect amount of time to travel around the country. My Taiwan itinerary included Taipei, Xincheng (Taroko Gorge), Kaohsiung, Tainan, Lukang, and Taichung.
I spent three weeks in Japan in November 2015 visiting Tokyo, Matsumoto, Takayama, Shirakawa-go, Kanazawa, Nara, and Osaka. This was my second trip to Japan in November. It’s a great month to visit, since you can still catch the changing of the leaves and the weather is cool and crisp. Possible downsides: The Japanese Alps region is already pretty chilly in November. Also, you may encounter hordes of leaf peepers, especially in the south where autumn color is still most vivid.