This question is much more complicated than it may appear. There are a number of factors here. Currently, I work in Manhattan for the summer but I live in NJ. Here's what you need to think about.
Transportation costs and time
If you live in NYC, traveling around with a monthly MetroCard is currently $89/month (but with talks of increases will probably be close to if not barely over $100 next year). Regardless of the amount, this is cheap. If you are going come from NJ, you need to find out whether you will drive into the city or take NJTransit. The closer you are to city, the cheaper your monthly ticket will be. If you take the Northeast Corridor line in, you'll be paying at least $116/month just to get into the city and if you're job is not within walking distance of Penn Station, you'll need a monthly MetroCard as well. I know that from New Brunswick, it costs $361/month to go to Manhattan on NJTransit. Here's the PDF for the chart:
http://www.njtransit.com/pdf/rail/R0070.pdfMy route is from the Upper West Side to Penn Station to New Brunswick. In all it takes, 1 1/2 hr to get to New Brunswick. Some times you wish you can be home in like 20 minutes. Too bad. No matter what, it will take me at least 90 minutes to get to New Brunswick from the Upper West Side. Transportation cost is $361 + $89 = $480/month.
Again, it depends where in BK you live and where in Manhattan, your job is cuz it take a while to get from BK to Manhattan depending on both. Regardless, you're still only paying $89/month to travel. In NJ, you need a car to get around; in BK, it's a luxury but you don't need it.
So if you have a place in BK that's not too far from Manhattan, you won't have to worry about long transportation times, switching from MTA to NJTransit trains, and shelling out at least $100 (and you can see up to and more than $350) for transportation. But if you live in Newark (or someplace close to NYC) so that you can take the train in, you'll probably pay around $150-$200 for your monthly NJTransit pass.
This is assuming that you're taking the train in. If you're driving in, there are tolls in and out of NYC that you need to account for. And if you plan on driving into the city, you should already know that parking is you know what.
If you hate long rides and/or if the difference in living in an apartment between NJ and Bk is less around $200, do the math and live in Bk. If you don't mind transportation and the difference in a Bk apt. and NJ apt. is greater than a $200-400, live in NJ.
Don't forget about state taxes and the fees that come with working in a different state. You will fall into different tax categories than your coworkers that live and work in NYC.
City vs Trees
You also need to know whether you like the city or you like trees. Every NYC resident knows that they need to spend some time out of NYC in order to see trees especially those who live in Manhattan. You always will need a break from the concrete jungle even if you love it. However, if you love the outdoors, NJ is your place for sure (unless you live upstate or in the upper part of the Bronx).
Food
If you know where to go, you can get good food prices in NYC. If not, you'll get ripped off paying a lot for a little. Generally, NJ has lower prices and you don't need to hunt around for good stores.
Entertainment
NYC wins...enough said.
At the end of the day, there is a lot to consider. Best thing to do is to make a chart of pros and cons and list all the expenses you anticipate to pay living in both locations.