That's a good kit. Your child is lucky to have a thoughtful parent like you. Just some random thoughts:

In the summer, the heat, humidity, and sun can be brutal if she needs to do a lot of walking or even just waiting around outside. I'd add sunscreen. A hat might not be something that she thinks to grab when she's gathering clothes if she normally doesn't wear one, although I suppose the scarves (thick wooly ones?) would do in a pinch. Water could be an issue, so just one canteen might not be enough. That's a tough call since water is so heavy. She could tire herself out just carrying extra water, particularly if she needs to hoof it out of the city.

Is she really going to use a poncho during a downpour? She'll be a hip little New Yorker by then, y'know. A small, but sturdy umbrella might be rain protection that she would be more likely to actually use. She could always leave it at her dorm if it isn't the rainy season. I really like my compact GustBuster umbrella. Super sturdy. After every windy storm, the sidewalks and garbage cans are littered with broken umbrellas, so a sturdy one is a must. Oh, and it could also double as sun protection in the summer.

I'd throw in a couple more flashlights, although not necessarily with a full set of extra batteries for each. She'll be with friends, hopefully, but chances are, a cell phone is the closest thing to a light source that anyone else will have. And when you're in NYC during a blackout, there are a lot of situations where you'll be in the dark, even during the day. Extra lights could really be handy for her to give out. Nothing fancy. Heck, even keychain lights would be better than nothing. I could easily imagine her traveling with a group of other classmates from NJ heading basically the same way to get out of the city and light is quite critical.

If they're available for her cell phone, one of those AA-powered external batteries (the Charge2Go is one example) would help keep her in touch for longer, particularly if her phone was already low when she needed to bug out. Personally, just based on my experience living through a number of events in NYC, including 9/11, having a radio to get information and a charged up cell phone to communicate were very comforting. Lack of information and the inability to communicate produce a lot of stress.

I might throw in some more snacks. During a long trek, the last thing you need to be is grumpy and frazzled from low blood sugar and stuck somewhere where you can't buy anything to eat. And again, there's a good chance she'll be with friends who might really need a little nutritional pick me up, too.