Its high density and superb transportation mean you don't need a car -- go almost everywhere with your kids by walking, bicycle, or extremely frequent convenient train. Riding in the car sucks for kids (and adults, IMO).
There is access to all kinds of world-class health care, and all of it is free for your kids.
Tons of great educational institutions from the best universities down to preschool (and although the preschools can take some time to get into due to capacity, they are by and large terrific).
Great food of virtually every variety except Mexican. Most of Tokyo is extremely clean, safe and crime-free. Multiple always-open industry-redefining convenience stores, same-day Amazon prime deliveries, synchronous 1Gbps fiber optic Internet connections for $50 a month, a regular taxi system that is better than the Uber you always hear Americans raving about, one-hour cold beer delivery... in other words, the kind of fundamental lifestyle convenience level that is good when you are single, but becomes way more important once you have kids.
Source: I live in Tokyo with my wife, 2-year-old, and 2-month-old.