The lists below are the things I have found here that interest me for our trip to Kyoto and Tokyo starting next weekend. I am looking for some help to group them in a logical order of how many and which ones to do each day. As in a logical progression so I am not running all over the place and backtracking. And don't hesitate to tell me to skip anything on the list as not worth it or to add in anything that is a must see/do. While these are all touristy things, we do like to wander around cool neighborhoods to get a flavor for real life. Not into anime or electronics.

Kyoto - 3 to 3.5 days (we are there for 6 but plan day trips to Hiroshima, Nara and there is the Jidai Matsuri festival on the 24th so that will include Heian, I guess. Staying at the Westin Miyako. I'd like to cut out ones that aren't worth bothering with. How to group these?
Nijo Castle
Nishiki Market
Imperial palace (not sure if it's worth seeing?)
Ginkaku-ji
Higashiyama
Sanjusangendo
Chishakix-in Temple
Kiyomizu-dera
Nanzen-ji
Gion - really want to see geisha
Kinkaku-ji
Ryoan-ji
Heian Jingu
Higashi-ji
Nishi hongan-ji
Katsura - have been trying to reserve a visit
Trip to Hikone Castle - worth it?

Tokyo - 3 days/nights at the Park Hyatt Tokyo. This is where I am really confused about how many realistically per day and how to group them logically as Tokyo is so vast.
Meiji
Asakusa
Senso-ji
Imperial Palace
Tsukiji - probably for breakfast, not getting up for the tuna auction.
Shinjuku, Shibuya crossing, Harajuku - just to walk around
Tokyo Metro building for viewing platform
Ginza
Yoyogi Park
Tokyo Station - because it sounds cool and for ramen
Yasukini Shrine

I know I have far too much so that's why I need help. I don't know what to skip (or what to add). We like to walk and take transit. And I am really looking for that hidden gem, the must-see, not-well-known thing that you've found.

Thanks so much for any help/advice.