The Tokyo area offers more of traditional Japan than you might think (Kamakura, Nikko, little pocket neighborhoods), and the Kyoto area offers more of modern Japan than you might think (Osaka and Kobe are just short train rides away).
To avoid that rushed feeling, read up on both Tokyo and Kyoto, pick one area, and stick to it. Both areas offer so much to see and do. Like one of the posters above, I have been traveling to Japan for many years, including some time living there, and there are still things on my bucket list in both regions.