Tokyo is a treasure chest of free entertainment for families with small children and far more green and imaginative than you would expect from a concrete jungle. The good news is, most of them are either very free or very cheap.
One recent trend is to bring more authentic natural playscapes into the city. Instead of plastic they focus on wood and water. Instead of safety they focus on being wild and slightly dangerous.
Heiwanomorikoen obstacle course
There are also a lot of playable sculptures such as the octopus towers,
each uniquely constructed by the Maeda Environmental Art Company.
Or the famous but slightly hidden Elephant Slides at
Shinjuku Ward Akagi Children Amusement
Pirates of Tokyo Bay are asked to enlist on the battle ship at Odaiba
Sea Breeze Round
New playgrounds are constantly being built, often after having consulted the local community as happened in FutakoTamagawa where a new water based park will finish construction later this year.