I've been in the big bad city for a few months now, and I must congratulate myself. I have not be mugged, assaulted or murdered. Thus my well-intending family's fears have not been realized, not yet anyways.
For non-native New Yorkers, moving to the city is a big deal people. "Oh you're moving to New York, be careful." Or, "New York is a scary place. Brave girl, I hope you're buying pepper spray."
I don't know what everyone is so scared about, the people of New York are genuine and kind people. Countless individuals have guided me on my misguided subway trips, a cash only newspaper stand gave me a water for free once he realized I was without cash, and yet another store clerk told me to take my rings off before I got mugged. See folks, givers.