I can't really say much for Nara, Hakone and Onimichi.
For me, I'm a nature kinda guy, I like my forests, gardens and parks.
For Tokyo, my favorite place was definitely my daytrip to Nikko. (I'm going to add >>7407347
to this post so I do 2 birds in 1 stone.)>>7404090 , >>7404091 , >>7404093 , >>7406293 and >>7406294 were taken at Nikko.
I also really hate tourists (I can see the irony) so my main advice is always when you go to places to take a look at side routes. Nikko's main temple was crowded af and I took a sideroute which gave me some shrines for myself and literally only seeing 2 other people in 1.5 hours.
The 5 buddha picture was taken at a sideroute shrine, it's also the grave of some monk if I can recall correctly.
Other place for tokyo is Rikugien garden, which I went to on a rainy day, which let me get that place all to myself as well.
Kyoto is going to be really busy, for some reason it always is. though you are coming at the right time (you dodged golden week you lucky bastard) so it isn't going to be at it's worst.
My favorite location in Kyoto was Fushimi Inari. But once again, I took different routes up the mountain shrine. The thousand gate part of it kinda gets repetitive after 15 minutes of climbing, so don't be scared to just wander off into the many different paths that you see lying next to the shrine.
I think that after Kyoto you will probably be kind of sick of shrines and Temples.
As I am currently in Osaka while writing this, I can give you some good ones here.
Really just take some daytrips from here. One of my favorite locations since I came here was definitely Kitano and the herbal garden at Shinkobe. This place really gives off that ghibli vibe. (I quickly edited 1 photo as my next pape so you can get the feel of it).
Other place I really love here was the Expo 70 Commemorative park. I walked around this park for 4 hours and I only saw like 2/3rd of it all.
Thats all really.