13 days japan itinerary check

I will be traveling to Japan April 9, arrive April 10 Narita Airport, I am thinking of spending 9 nights in Tokyo (check in 10th April, check out 19th April), 4 nights in Kyoto (19th April till 23rd April check out and head to Narita Airport)

in Tokyo:

Friday 10 shinjuku and shinjuku park and area around the hotel
Sat 11 Harajuku (takeshita dori, meiji) and Shibuya
Sun 12 Akihabara, Ginza
Mond 13 fuji Mt day trip
Tue 14 Asakusa, ikebukuru
Wed 15 Disney sea day trip
Thur 16 shibuya for shopping
Fri 17 tokyo university (for my husband, he might study there)

Sat 18 tokyo dome

Sun 19 check out from tokyo early and leave to kyoto
Mon 20 kyoto
Tue 21 kyoto
Wed 22 kyoto

Thur 23 head back to Narita airport


please advise for places and attractions, and if I should change the plan and add more days to kyoto
also we would like to book a private onsen, something luxury

for the hotels I couldn't decide if I should stay in shibuya or more quite place, and what do you think of Minato area for basing

Personally, I would definitely add more time in Kyoto.
I�fm not sure what you need to see and do in Tokyo, but I would perhaps rearrange things
Friday 10 shinjuku and shinjuku park and area around the hotel
Sat 11 Ikebukuro, Harajuku (takeshita dori, meiji) and Shibuya
Sun 12 Asasukasa, Akihabara, Ginza
Mond 13 fuji Mt day trip
Wed 15 Disney sea day trip
Fri 17 tokyo university (would you need a whole day for this?with NOTHING else? ) Tokyo Dome then Shibuya if you really need to return
Sat 18 check out from tokyo early and leave to kyoto
Sun 19 Kyoto
Mon 20 kyoto
Tue 21 kyoto
Wed 22 kyoto
On one of these days you could consider a day trip to Nara.
AND a 7 day JR Pass will pay off from Tokyo-Kyoto and back, esp adding in the Narita airport trip as well,
Thur 23 head back to Narita airport: change trains at Shinagawa: its much easier than in Tokyo Station.

To me, that is a lot of time in busy Tokyo: I would actually consider Nikko and/or Kamakura day trips and drop half the shopping areas, but thats just me.

Enjoy!

thank you so much, what about private onsen, something very nice, but without the need for staying in a hotel or ryokan just visiting for few hours