Having been raised in Manhattan, I firmly believe that it's not only a good place to raise children, it's a fantastic place to raise children. If you can afford it, that is. Which is, needless to say, a very big if.
I don't have any wee ones, but one thing I will never understand is why suburban America is almost universally considered to be the ideal place to raise children. Yes, the money issue in cities is real, so I understand why people choose the suburbs over the city, but the money isn't the reason which is usually given. The entire suburban aesthetic is thought to be good for kids. Don't get it.