Do Nikko as an overnight trip. Skip the night by Fuji altogether. Go directly from Nikko to Kyoto. Give yourselves two nights on Miyajima to allow yourselves to see Hiroshima city the day before your first night, then a full day relaxing on the island. After Miyajima you could head further west to Fukuoka. Get a flight from Fukuoka via Tokyo or Seoul back to the USA.

BTW - Could you stop copying and pasting the entirety of every comment that has been posted upthread?