Cruise, Mt. Fuji (and regional area), Hatto Bus tours, Digital Art museum, Ramen museum, Akihabara (anime, Manga, electric street etc), Shibuya scramble crossing, Shibuya on a weekend night, Mariocart, Harajuku shopping/nightlife, Yoyogi park (street art, dancers etc.), Tokyo Disneyland and Disney Sea (if they've grown weary of "culture"), Taito (huge Gundam robot), Rainbow Bridge.

Kyoto area (hub for day trips):
Kiyomizu temple, Nijo Castle, Imperial Palace, Kinkakuji, Maiko show (geisha in training), Nara (feed deer, Daibutsu), Hiroshima Peace Memorial, Itsukushima shrine (hike also recommended), Arashiyama (Bamboo grove, Monkey park - includes short hike, oldest bridge in Japan IIRC)

Remember to use cash. It's the preferred way to get around (or you can get one of the many cash cards in Japan). Also get data for your phone... usually available in the airport.

[I'll update this later]

https://www.youtube.com/watch?v=iUi45VkLhFg

https://www.youtube.com/watch?v=Pfjbv6_e2zc

https://www.youtube.com/watch?v=IsngamFa1ps