Grew up in central Jersey, I would have no issue raising my kid there whatsoever.
I swear, everyone posting with "BUT I CAN AFFORD IT" is absolutely tone deaf to the US housing crisis we're in.
(But man, have things changed. I grew up in central Jersey in the 80s, and back then no one of any means wanted to live across the Hudson from Manhattan. Nuts to see that now many people are priced out of that area.)