Frankly, I can't imagine only spending 3 days in Tokyo and Kyoto but different strokes for different folks.

As mentioned elsewhere, there are several options for day trips from both Tokyo and Kyoto. For such a short visit, I wouldn't suggest changing hotels more than necessary as that just eats up visit time and burdens you with luggage more often. From Tokyo, you can spend a full day visiting Nikko, Kamakura or even Hakone. I suggest Nikko, which is in the mountains, for natural beauty plus some historic temples and shrines or Kamakura, near the coast, for very old temples and the ancient seat of government. Kamakura has the outdoor "giant Buddha." From Kyoto, short day trips are easy to Nara, the first capital of Japan with its sights all concentrated in a park, Osaka for high energy, big city life or Himeji with the walkable castle and grounds. All would be reachable on JR trains, using a JR Rail Pass. From all of those choices, you can simply return to your hotel in the city when you are tired of sightseeing.

JR