Tsumago would work best if you went to it between Tokyo and Kyoto, because that's where it's located.

There's no need to switch hotels between Kyoto and Osaka. They're an hour or less apart by train.

A two-week rail pass should be sufficient. Within Tokyo itself, a Pasmo/Suica debit card is more useful, because it gives you access to all surface trains and the subway system in the Tokyo-Yokohama metropolitan area.