Yes, definitely bring your credit card with the biggest limit, plus a healthy amount of cash. New York is expensive.
The general fear and loathing I see here regarding New York City is quite amusing. My family got off the boat in NYC back in the 1920's and never left. Although I myself now live in the Philadelphia area, I am a native-born New Yorker, and I did go to high school in Manhattan while living in Queens (College Point, to be exact, and Stuyvesant Class of 1986). No city on the face of the earth is probably safer than New York City. It's quite surprising, really, how New Yorkers will help each other and visitors out. Not to mention the huge NYPD and NYFD (my grandfather was a Battalion Chief).
And, of course, crime since the reign of Rudy has been pretty low. Just don't carry a firearm or a locking knife longer than 3 7/8" (4" is the limit). You will notice that most locking knives on the market are no longer than 3 7/8" for just this reason. The NYC Custom Knife Show posts big signs concerning the laws of NYC...
Oh, and buy some subway tokens. They're going out of style quickly, and the subway really is the best way to get around.
Especially in the post-9/11 NYC, New Yorkers really know how to pull together when needful. Yes, there are some bad areas, but you probably won't find your way to them--they're off the beaten track...well, except for Times Square--I wouldn't expose children to that pit of Disney iniquity!
Go see Ground Zero, if you haven't already. Go to the top of the Empire State Building (actually, you might want to avoid carrying a knife to the tourist spots). Go see Lady Liberty. Go to Central Park (but not alone, at night). Drink it in--it's the Center of the World.
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Gemma Seymour (she/her) @gcvrsa