don't teach her to carry concealed...if ANYONE spots the gun the cops will be all over her and she'll be looking at 3.5yrs minimum. if she has to use it in defense of herself...same deal. guns are no joke in NYC...don't mess around.
she can probably get a permit for the home but not to carry out and about. long gun permits are easier to get.
if you can get her a NYC permit i would be quite surprised...most mere mortals are denied as not being sufficiently "privileged" people.
your best bet is to:
1. give her lots of money so that she can take cabs at night.
2. give her lots of money for rent so she can live in Manhattan below 96th street where she can hail said cabs to/from reliably.
3. give her lots of money for rent so she can live in a doorman building.
4. make sure she learns some street smarts and learns to avoid the usual crimes...drugged drinks, push-ins, tailgating into non-doorman buildings, etc.
5. tell her to not drink to excess...it's VERY easy to do since the #1 employer in the city is restaurants/bars. that's what she'll spend most of her money on (aside from rent). it's usually the women who get plastered that end up getting victimized by strangers and acquaintances...and police (at least two recent cases of NYPD officers raping women while on and off duty).
give her lots of money...NYC is a playground for the super wealthy. young women are victimized at an alarming rate there but it's really not that scary in the nice areas...it's not baghdad.
fear of crime isn't a good reason to tell her not to work there out of college. NYC is full of career opportunities for young motivated people, she will have a bright future. MILLIONS of young women live there and do just fine.