Is my 15-day itinerary sane?

I'll be in Japan in the second half of October, and my itinerary looks like this –

1. Day 0
   1. Land in Tokyo
   2. Immediately leave for Osaka
2. Day 1 (Osaka)
   1. Kuromon market
   2. Teamlabs
3. Day 2 (Osaka)
   1. Osaka castle
   2. Dontobori
4. Day 3 (Osaka)
   1. Aquarium
   2. Tempozan ferris wheel
   3. Universal studios (not very sure about this one)
5. Day 4 (Kyoto)
   1. Fushimi Inari shrine
   2. Nijo castle
6. Day 5
   1. Day trip to Himeji
7. Day 6 (Kyoto)
   1. Just walk around in Kyoto and chill, recover from last 5 days of travel
8. Day 7 (Hiroshima)
   1. Visit peace memorial park
   2. Lunch at Okonomimura.
   3. Hondori Shopping Arcade
9. Day 8
   1. Day trip to Miyajima island
      1. Itsukushima shrine
      2. Hike up mound misen
10. Day 9
    1. Hiroshima castle
    2. Prefectural art museum
    3. Shukkei-en Garden
11. Day 10, 11, 12, 13, 14, 15 (Tokyo)
    1. I've always wanted to go to Tokyo, and I don't want to plan the specifics for what I'll do in the city. I want to take my time and explore the city as it comes. I know I want to do the following, but in no particular order –
       1. Visit Teamlabs tokyo
       2. Walk around Shibuya
       3. Tokyo Skytree
       4. Shinjuku Gyoen national garden
       5. Imperial palace
       6. Sushi at Tsukiji Outer Market
       7. Day trip to see Mount Fuji

My goal when travelling to any country is to experience things that I can only do in that country, so for Japan I want to do things that I can't ever do outside Japan. I'm primarily going because I'm very interested in the culture and the food. I don't know much of Japan's geography, though if there are sights that are unique to Japan (like Fuji), I'd love to see them.

I have the following questions about this itinerary

1. I have been considering going to Fukushima instead of Hiroshima. Does that make sense given my travel preferences? From what I've heard and read, Fukushima is good for trying out fruits, a hike and sake. Is there more to it?
2. Is there something very obvious that I'm missing in all these places? Anything that I must do, but am not?
3. Is there something in this itinerary that I shouldn't do?
4. Am I spending too much time in Kyoto? Some of my friends who went to Japan said that Kyoto isn't worth more than a day unless you're in Japan for longer. Is this true?

TIA :))