If you've raised them with this attitude, then perhaps they wouldn't.

With our own kid (and I am sure she is no way unique), there has always been a direct and unquestionable correlation between the price of the food and the size of her appetite, particularly in Japan, and particularly when many small dishes are served.

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jazzah
The absolute lowest you can go for budgeting in Tokyo is (price per person):
Meals - you could realistically have lunch and dinner (and a snack or two) for 4,000yen a day, can be done for less (really squeezing it), obviously you could spend a lot more.
Transport; budget between 400yen and 800yen a day - depends on your itinerary
Cheapest way to buy a weeks worth of activities is to get the Grutt Pass - it allows entry to a huge array of museums and attractions for 2,000yen
https://www.rekibun.or.jp/grutto/pdf...o_pass2015.pdf