Of course, there's a wide range of possible prices and options, and things will vary according to the current state of the real estate market.
Office space in New York is quoted in dollars per square foot per year. Usually you'll want around 250-400 square feet per person. Different offices have different amounts of usable office space, so YMMV.
The cheapest real estate you'll find that's reasonable to use for an office in New York is in Midtown South, including the Garment District, where you will find loft-like space for about $20/ft.
If you want nicer space, maybe in a class A highrise that is reasonably modern, downtown New York is a good choice, where you can find space around $30 - $40/ft.
The fanciest, midtown class A space is generally going to be around $50 - $70 these days. Of course, if you are a hedge fund, the sky's the limit, you can easily spend $90/ft or more.
But if you're looking to build your startup in New York, it's safe to count on the range of office space prices to be $20 - $45 per foot.
An important thing to remember is that THIS SPACE ISN'T USUALLY BUILT. If you care a lot about what your space is going to look like, you're going to have to build it yourself. That can cost anywhere from $100-$300 per foot or more depending on how nice you want it to be. A major part of negotiation with the landlord is over how much they will contribute to building the space. This is called a "work letter".
If you're lucky and you find prebuilt space that suits your needs, you may just need to paint and recarpet it. Plan on about $20/foot if that's all you're doing, and the landlord should certainly pay for that.
To save money, look for sublets. The biggest cost savings with a sublet comes from the fact that the space is already built.
[UPDATED NOV 2010 TO REFLECT CURRENT MARKET]