One of my kid’s favourite parks within Tokyo when she was about 4 years old was the Nikoniko Park at Meiji Jingu Gaien and there is the Mitsui Garden Hotel Jingu-Gaien Tokyo Premier just close by.
Closest station is Shinanomachi JR & Kokuritsu-Kyogijo on the Oedo line is also close by. See posts below

Only problem is that the playground was closed around the time of the Olympics and it appears to be in some kind of “soft” re-opening at the moment.

I cannot tell at all what the likelihood will be that the OP’s kids would be able to use this park next October. Does anybody know any more about the restoration of this facility?