Like
@limr said. I wouldn't consider "no eye-contact" to be the end all answer to personalities, or any type of negative connotation. It's just something that's not done, because people have places to be and there are literally millions of people in the City. It's quoted that 8 million people ride the subway
every day.
When driving, if you don't take your chance, you'll be passed. It's not that drivers are less courteous, or meaner, it's that there are so many cars that you have to go when given the chance. That chance is usually a second or less. You want to change lanes? Put your turn signal on, and merge in. No one is going to hold your hand while doing it. We're all adults and treat each other like it.
NYC isn't a zoo, and it's not "scary". It's a city full of people, normal people, like you and me, just trying to live their lives.
The wife and I frequent all the time (the wife grew up in Brooklyn and still has family there). People hold doors open, apologize when bumping into you, stand to the right on all escalators to let people walking up the escalators to walk past on the left, and let people get off the subway first before trying to enter.
Rarely do I make eye-contact or say hello to people in my own neighborhood in the suburbs of Central PA, let alone in a city with millions of people. Walking through Target? I don't say hello to anyone, why would I? We live in close proximity, we're not friends. I do wave and say hello to direct neighbors; I'm not an as5, and I like my neighbors. The same happens in NYC. It may not seem like it to visitors, but those who live in NYC know the people living on their block, living in their building, and thus are courteous to them as you are to your neighbors.