The JR Railpasses are the way to go if you are doing stuff like Tokyo to Kyoto and back (or vice versa). The shinkansen trains are fast..... and why waste time traveling on trains using locals to save a few bucks? (If you are staying in eastern Japan long.... make sure to check out the JR East railpass options too.)
In Kyoto and Tokyo.... I'd be looking at the potential food budget you have. Now, for SURE you can eat very cheaply; there are tons of little noodle shops, stand-up ramen places, cheap isakaya, and other such. God forbid... there are McDonalds, Mosburgers, and Starbucks too
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But one of the best things about Japan is the food. In Kyoto kaiseki cusine is phenomonal .... but typically is expensive for the good stuff in the good locations. Really good tempura and sushi and sashimi are all also expensive. And something like the good kobe beef in a good place...... you often need a mortgage
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Yes... you can find cheap kaiten sushi that is far better than most resturant stuff here in the USA........ but sushi from a good place makes that kaiten stuff seem pretty mediocre too.
A couple small bottles of good Nihionshu and a pile of yakitori or kushiage in an izakaya in Tokyo or Kyoto for dinner can easily run up a bill of 4000 円 or more. With the current crappy exhange rate..... that comes to something like $50 - 60 USD. While a great dining experience...... and often some GREAT food...... that is not exactly a top end resteraunt.
If this is a "big deal" trip.....then try to plan so that you are not always wishing that you were able to do the things that you want to do. Save the pennies before you go.
best,
...................john