Hi BillieJean!
Welcome! Wow, looking at colleges in NYC!!! It's a great city for young people. My daughter has lived there for the past three years and loves it!
I just got back from a quick visit there and tried to pay careful attention to what people were wearing. I second Ele in that NYC can be very hot in the summer. It also gets very hot on the subway platforms. Most young girls (and women) were wearing sundresses and skirts. I also saw a lot of jersey knit dresses, like the ones you would find at stores like jcrew or the Gap, paired with flats. The dresses and skirts will also be appropriate to wear if you are planning on taking any campus tours.
Here are some examples of what I mean:
http://www.jcrew.com/AST/Brows...../16631.jsp
http://oldnavy.gap.com/browse/.....=662306022
A little dressier than shorts but still cool and casual. These are just to give you an idea of what I'm talking about. I'm sure there are more youthful versions. I realize that you are only 17.
That said, the attire was definitely more casual in the summer than when I was there in March. A pair or two of nice shorts would be fine. I would bring your skinny jeans but you may want to save them for the evening when the temperature cools down a bit. I didn't see many scarves, it was just too hot.
As for footwear, I saw a ton of flat, casual sandals, ballet flats and converse sneakers. Metallics were everywhere! I did see women in heels but many of them were on their way to work or didn't look like they planned to do a lot of walking. Keep in mind that you'll probably be doing lots of walking and taking campus tours. I don't think I saw any boots. I would suggest saving them for fall.
Hope this helps. Good luck with your trip and college search. If you get a chance, go to the top of the Empire State Building at night. The view is breathtaking!