It depends on the neighborhood, I’m in nyc often and I feel safe most of the time. The worst I usually see is maybe some homeless mumbling to himself or New Yorkers being New Yorkers. No big deal. The drivers , specially cab and Uber drivers are dangerous though , they have no regard for people crossing the streets . You’re not exaggerating on that part , is almost the same in Jersey, but since there are not that many pedestrians it doesn’t seem as bad . But we have bad drivers all over the tri state area and other cities in the US as well