Don't let these folks scare you. You can rent an apartment under $1000 in decent parts of Brooklyn, Queens, Harlem and even Jersey which are all 15 to 25 minutes away from anywhere you want to go in most of Manhattan.
Those areas are not all scary, you would be pleasantly surprised what you will find. Tons of NYU students discover this every year.
After that, $76 for your metrocard will take care of all of your transportation needs. I mean all of them... no where else has the quality public transportation that NY does. Millionaires take the train here every day if that's any indication of what to expect. It's not like other places where you need a car. People don't even expect other people to own a car here. It's like no where else in that regard.
Food can be had for normal anywhere USA prices. Whatever you are spending where you are is what you can expect. Plus, NY is the king of the best cheap bagles and pizza everywhere. $2 will fill you up anytime of the day and you can do it on virtually every block. Ya can't beat that.
As far as entertainment you will be ok with very little money. Check out
www.villagevoice.com or
www.timeout.com for listings of cool things to do that don't cost a lot of money.
And if you really wanna save money, get a girlfriend on orientation day. Another NYU freshman will live the same way you do and not expect much from you. You two will enjoy just exploring the city for a year or so.
Oh, I forgot one key thing, if you want to find a good, but cheap apartment you really should pay a real estate broker. Nice & cheap places exist, even in Manhattan but you are gonna need some help finding them.
www.citi-habitats.com is probably the best at finding them. You can also use the search on
www.NYtimes.com
Enjoy.