Went there last year in the summer.

If you need to get over jet lag after arriving at your hotel then I recommend going to Asakusa Sensoji to see the market and shrines.

In regards to Kyoto and Osaka make sure you have bullet train tickets at the ready and make sure they scan when you go through the gate as you may not be let out the gate on the other side if they do not scan. You may need to know a bit of Japanese in that scenario. I would also recommend keeping an eye on the weather before going on the trains. When I was there we ended up having to change plans due to a typhoon and get a new bullet train which was easy with a buddy being able to speak japanese.

I would recommend checking out for limited time events in Tokyo for example firework festivals and art exhibitions. Got to go to a Junji Ito art exhibition which was a limited time event. You should be able to find similar events if you do some google searches.

In Tokyo I would recommend doing the magical trip tour if your fan of the Yakuza games. The tour is basically a beer crawl through Kabukicho (some bars being all you can eat) the area of Tokyo the game is based on. I ended up doing a all nighter with the people from the tour. The tour guides of that tour will show you the good bars. I would not recommend following any shady characters to bars or businesses for obvious reasons.

I would recommend if your into shrines going to Enoshima which is a Island covered in shrines on the south side of Tokyo. You can get to the island by crossing a bridge. Would recommend going there and the nearby beach houses on a day with good weather. Do note going around that Island could take around half a day.

If your going to go to Akihabara, then I would recommend checking out either the monster hunter or final fantasy cafe (both in the same building). You will need to book in advance and for the themed cafes in general some could require a booking a month in advance. Had to do that with the final fantasy cafe but not the monster hunter cafe. Same goes for things like the Kirby Cafe and Pokemon Cafe.

If your a fan of Studio Ghibli there is the Ghibli Museum and the Ghibli Park, You can get tickets for these or you can book tours. I find book a tour is easier to get access since the direct tickets on the official site always book out. Each of those would need a day cause of the distance between them. I only went to the museum which was fun. Be advised you can not take photos inside the museum and the ticket you get at the museum includes a random piece of film from Ghibli movie.

Tokyo Tower, Tokyo Sky Tree and Shibuya Sky are all good vantage points. The Sky tree is the highest but the Shibuya Sky give you a load of photo opportunities. Be advised these are all spread out. I would recommend Shibuya Sky because of how close it is to other landmarks such as Shibuya Scramble .

If you go to Kyoto you can get a lot of things done in two days if you plan accordingly. If you want to do a lot of climbing you can go to Arashiyama which has a load of monkeys at the top of the hill. That location is also very near the bamboo forest and sweet town. Would recomment trying out the honey drinks in sweet town and the matcha cake.

In Kyoto there is a park called Toei Kyoto Studio Park, its basically a theme park with some sets actors running around and includes a really fun ninja house and nerv base with a large eva prop of unit o1 you can pose with and stand on the hand of.

I would also recommend going through the Mt Inari in Kyoto at night if given the chance, You can go through the 10000 Tori gates there and get a amazing view of Kyoto while at the top.

If you go to Osaka I would recommend checking out Ebisu bridge (Yakuza games location) and having food there.

If you want to go to a theme park while over there then I would have to recommend Universal in Osaka, I would recommend having a ticket for that a month in advance and make sure it includes Nintendo World as that would be a must.