KingslandBarge Just did a 3 weeks in Japan last year and here are my recs.
Osaka - Umeda Sky Building, Osaka Castle, the theme parks and then mostly others are food. Visit Kuromon Ichiba and feast there one afternoon. Ajinoya Okonomiyaki, Oretachi No Curry Ya and Kushikatsu Daruma are must tries. Also try mario kart if you have time, it's cheaper here than Tokyo.
Kyoto - Rent a kimono and walk around Gion if you wish, otherwise Yakasha Shrine, Kiyomitsu-Dera, Fushimi Inari-Taisha Shrine (just cut across and go to the middle for a nice photo spot), Arashiyama (go early if you want to skip the crowd) are must visit. Pick a restaurant to eat at the famous Pontocho street. If you have patience to queue, you can try the world renowned Kichi Kichi Omurice. Also consider a day trip to Nara.
Tokyo have too many things to do, I will reccomend a few things that you must-try. Red Rock Steak, Suzukien (7 levels of Matcha ice cream), Ichiran Ramen, Torikatsu Chicken, Gyukatsu Motomura (prepared to q) and Tonkatu Marushichi (giant tonkatsu). Also, not many people knows this but since you are visiting during Sakura season, you can go to Chidorigafuchi to rent a boat and moat around the river full of Sakura in the evening its amazing.
Would also highly reccomend you to take a day trip to Fuji, one of my favorite places in Japan. Try fuji-q if you dare.