Osaka is good, but you could really just go to Dotonbori, see the cool shop fronts, eat okonomiyaki, eat tako yaki, and be done with it. One day would be anough and it’s close enough to Kyoto that you could do that.

Kyoto is great for cultural temples and castles… you will wish you had more time to see them. I recommend Nijo-jo… the squeaky castle… not as popular but by far the most interesting think I saw in Kyoto

Tokyo’s great for the modern stuff… and much more nightlife. Make sure you see Harajuku, Shimokitazawa, Shibuya and Akihabara.

I’d do 3 days Tokyo, 3 days Kyoto and maybe a day tip/overnight in Osaka.

Get yourself a Japan rail pass, it’s totally worth the money.