three mounths in Tokyo. How lucky you are!!!
Well, for those i've seen in Kyoto, I would suggest : Toji temple (+ a very nice garden, really peaceful, i liked it a lot; do not miss the cemetery just behind it, some funny graves (I know it sounds awkward). it is on the UNESCO list (world heritage).
Nijo Castle, Kyoto Imperial Palace, Chion-in temple (if you are lucky you may see people in traditionnal costumes for their marriage). I would also suggest Kyoto station (i adore the architecture, especially at night, but I guess you have already seen it). and why not the international manga museum (or whatever name it could have).
If you are in the area, what about Nara : have you been there? There is also Osaka (do not miss the floating garden observatory on Umeda Sky Building , no better view of the city! though it's better if you have a beloved one to go with).
Feel free to ask if you want more info about Nara. i would'nt be of any help in Osaka, I spent few times there.
And have a good trip.