I am not really asking for the plausibility of the Japan's conquest of the following territories.
Lets say that a unified Japan (time period is in your hands) manages to conquer/vassalize Korea, Greater Manchuria, and the Mandarin-speaking parts of China and successfully sits the Yamato Dynasty on the Dragon Throne
This becomes a culturally diverse empire with a Japanese ruling class lording over millions of Chinese, Koreans, and Manchus. Kyoto and Tokyo seem like too far away to to successfully administer the rest of China, but would they keep either of those cities as the Japanese capital? Or would some other place be a better candidate? (Seoul/Nanjing/Beijing, etc.)