I spent three weeks in Japan in 2015. My two cents.
I handled Kyoto/Osaka as one destination. 15 mins commute on their high speed train. Days were spent in Kyoto -- great for nature and temples. Back in Osaka for dinner -- great food, vibrant nightlife and more abundant and cheaper accommodation options.
Kyoto lunch at
http://www.tripadvisor.ca/Restaurant_Review-g298564-d1173251-Reviews-Yoshikawa_Inn_Tempura-Kyoto_Kyoto_Prefecture_Kinki.html
Get there early at 11 (no resos at the counter). The guy is a tempura master. Constantly adjusting the oil temp so that the batter is never greasy or heavy. Only the freshest ingredients (seafood, veggies, legumes, nuts) get the treatment. He hands you one finished item at a time. Mind blown.
Tokyo is out of this world. You'll discover your own path, and it'll be amazing. I would avoid getting up at 5am to check out the mega hyped tuna auction at the overcrowded fish market . The sushi is great almost everywhere. if you want the ultra fresh affordable sushi breakfast, the fish market Osaka delivers the same taste (sans lineup)
My fave Tokyo hoods were classic Omotesando/Harujuku and
Shimokitazawa -- think of a rundown East Village from the 90s where every store is a vintage shop or a live music venue. There is a crazy coffee joint (with the only rude store owner in Japan) where you can get patented espresso shots. Check his website for hours when he's serving up his precious
http://www.bear-pond.com/
I would spend whatever time left over from Tokyo and Kyoto/Osaka down south. Miyajima is a great scenic spot to just chill and refresh for 24-36 hrs
I really loved Kagoshima. Ate like a king for about half of what it costs me in Toronto. Also enjoyed Fukuoka and Kumamoto. Even the food in Tokyo was affordable. For example, at Bistro Jill, I ordered a duck leg stuffed with some Foie for $18 (tax and tip included). In Toronto, I'm paying at least $35 plus tax and tip.
Final thoughts.
Order a mobile wi-fi thingy.
https://www.globaladvancedcomm.com/index.html
I paid $80 for unlimited data. It was waiting for me at my first hotel (and I gave the delivery envelope to my last hotel) You'll never get lost with google maps and you can use tabelog (Japan's yelp) to point at food shots so your waiter can figure out what you want.
As Hoglund said, travel light. I packed a week's worth of clothes in a weekend bag. Got my laundry done at one hotel, did my own laundry at my Kagoshima hotel. Picked up a few emergency tees at Uniglo.
Look into a 2 week rail pass. Those high speed trains make zipping around the country a pleasure.