I'm from Farmington, CT... & I'm doing 2 months in nyc this summer. Going for either an internship for Fashion Marketing at Saks or to work. I'm there every other weekend basically.
Jobs: In the summer, not that easy unless you know people. If you're trying to work at a high scale boutique such Bape, Y-3, etc... forget about it. No chance unless you have connections. Cafes or smaller chain shops such as American Apparel, Urban Outfitters, etc.. then possibly
Apartments: Simply put, not cheap. Depending on what you're looking for, & seeing it's only you two, then about $3,500 a month for rent. BUT, that depends on your location. You wont find an apartment in tribeca or soho for that much. Also, know if you want a furnished or unfurnished one. Furnished will cost more. It's best to just search around online.
Cost Of Living: Transportation is easy so no need for a car. A metrocard will set you back $110 i believe for unlimited rides. Get a bike too if you'd like. Food isn't much more expensive than everywhere else, & I'm talking about grocery store prices. Restaurants aren't usually cheap, but you can find awesome pizza places that sell pizza for real cheap (i believe it's 51st & 2nd that has a little pizza restaurant where it's $1.50 for a HUGE slice, & I mean HUGE. A Large is only around $10 too.. so not bad at all)
I just think the hardest will be finding a job. I'm going in the summer (not sure when you are), but during that time, all college kids go there to intern & work, so jobs go quick. Same with apartments. If you find one you like & for 100% will be doing it, don't hesitate.
I'm going with 3 other people.. so we will be renting an apartment that costs around $10,000 to $13,000 a month... & in soho most likely. But, that's not way too horrible split between us all. We haven't found one yet, but, like I said.. some stuff can be cheap, some can't.