Interesting itineary.... a few comments:
Much as I like Osaka, the shrines and temples are nowhere as interesting as those in Kyoto. What I like in Osaka is the hustle and bustle of the Dotombori area (including the roofed over pedestrian streets) and also the underground malls in Kita, along with the Umeda Sky building and the Hep five Ferris wheel. The Castle is interesting but from the outside only. Check the enormous stones used to built the walls of the moats.
Kyoto: If the weather is nice try to go all the way up to Mt Inari and go down and around by the back way. It takes 4 hrs but is worth doing.
At the very least walk up to the highest view point with a great view of Kyoto.
I didn't find Nagoya that interesting. I would skip it unless there is something that you must absolutely see. I had rather go through Nagoya and stay overnight at Matsumoto to visit its authentic castle the morning after, then go to Tokyo via Nagano (without staying there, only changing trains)
In Tokyo it will never take you a full day to visit Asakusa or Akihabara or Ropongi or Harajuku (do visit the Meiji shrine after watching the Cos players. They stand on the bridge to the shrine)
You can spend some time in Asakusa each morning and evening for 1 1/2 hr, before and after a visit to someplace else.
Instead of the Imperial Palace gardens ( you don't see the palace and by that time will have seen gardens in Kyoto etc. plus it is a long walk from the nearest subway or rail station to there) and Roppongi (too many Caucasians making fools of themselves) I had rather take a boat from Asakusa to Odaiba and explore the various sights there, including the great Toyota showroom with cars we don't see anywhere else.
You could tack Shibuya to the first Sunday as it is the next stop after Harajuku on the loop line. Not a huge lot to see there either so you will have time.
This way, on the day you visit Shinjuku, first stop in Yanaka (
http://www.digi-promotion.com/tokyo-neighborhoods/yanaka/0 a lovely old fashioned area that look like pre-war Tokyo.
While in Ueno, be sure to visit, in the late afternoon, the Ameyoko-cho shopping area under the elevated JR tracks, just outside the Ueno station, in the direction of Akihabara.
http://www.japanvisitor.com/index.php?cID=357&pID=996#ameyok