What Should a Teenager Wear in NYC?

I wouldn't opt for the skirt. If I were you I would pair basics. A fitted gray tee and nice black pants with a few simple accessories can be simple and not cost a lot, but it looks put together. That's just one example but there are a lot of things you could do. Don't worry too much about detail, just do what you're comfortable with because you'll wear the clothes again and you'll enjoy your trip.