A block and a half away is one of the best playgrounds in the city, and three blocks the other direction is another fine playground. Both of them are packed with kids at all hours of the day. When we go visit family in the midwest, we make a point to take walks and visit the neighborhood playgrounds. We're almost always the only people there. Of course people have their yards so nobody needs the playground... I think something is lost.
Walk a few blocks in any direction from our house and you'll see tons of wonderful daycares, family-friendly restaurants, and other parents' necessities, most of them locally owned and operated by another member of the community.
We travel all around the city, we take the train. My son passes the time on the ride charming the other passengers and subway surfing. It's much more civilized than strapping him into a car seat and not looking at him for an hour every day.
I'll grant you that New York City is something of an outlier as far as American cities go.