I most definitely would not let my children go anywhere alone until they reach an age where I can trust them to be somewhat responsible.
Of course it all depends on the circumstances: the distance involved, the roads to cross, the local population, time of day…
Here in Gateshead there are several busy neighborhood roads (not busy by NY standards though, I guess) – for example Coatsworth, Whitehall, and obviously Prince Consort Roads – and almost no marked pedestrian crossings. And even if there were – a significant population in the area consists of not really upper class non-Jews, some of whom are plain criminals and quite a few of them – the youth especially – drive extremely recklessly.