I’m a current freshman at NYU. I don’t have a job this semester (still getting adjusted to everything else about moving away from home), but I did work over the summer and saved up a little over 2k. My parents are giving me fifty a week, and out of that I usually put away ten dollars in my savings and then buy a discount movie pass (I’m a film major, so I usually go to a movie a week and put in my budget). The remaining thirty makes things a little tight, but I manage just fine. I also have an emergency credit card, which my mom has allowed me to use for things like cabs to and from the airport when I visit home and to purchase some winter clothes (I’m from Florida, and don’t have anything for cold weather!) Other than that, if I want to treat myself–buy something that’s not a necessity or go to a show–it comes out of my personal savings.
Keep in mind that I’m a dorm with a generous meal plan and I don’t really drink/party/shop–my leisure activities are mostly film-related, and thanks to NYU discounts that’s no more than ten bucks a pop. This also isn’t factoring in books, school supplies, or regular subway fare (I do have a MetroCard that I refill occasionally, but my dorm is walking distance to all my classes and I don’t yet commute). Really, it’s all about planning ahead–buying MetroCards and movie passes when you have the cash, checking the NYU websites to see what the school is offering for discounts or for free, etc.
If you want to limit your kid’s spending but also have them experience the city, my advice is have them ask for tickets as gifts. Last birthday and this Christmas, I asked my parents for pairs of Broadway tickets. I was also given gift cards to CVS and The Container Store by family members, which are especially helpful when moving in–and a good campus cash alternative if you want your kid to have enough for grocery/toiletries but don’t want them to be wasteful. Look up whatever’s near their dorm, and send them a card a month to cover that sort of thing.