Having been to both, I certainly prefer Kyoto. So much beauty. My favorite place was Arashiyama and the bamboo grove. http://en.wikipedia.org/wiki/Arashiyama. But it is all good.
If you have a love for countryside, Hakone, around the base of Fuji might be worth a stop between Tokyo and Kyoto. Personally, I love the onsen in the countryside, sitting in a big hot bath gazing at the scenery around you. Sex segregated, you need to have some tolerance for being naked with others as well as very hot water.
Even in a city, the bathhouses are an incredible experience.
Do some reading on manners. Incline your head as you are greeted entering a shop. Wear slip on shoes, and be good at donning and doffing as needed. Know that bathrooms have a separate set of slippers. Stay in a ryokan?
Wander, and don’t let your days be time pressured. There is much beauty in the details in Japan, the neighborhood gardens in Tokyo, the shrines and temples, the average street. Visit the basement of a department store and sample the food. Kyoto, decades ago had great department stores, and I assume that has not changed.