If your company already has an office in NYC, can you look to the people responsible for hiring there to give you hard data on the number and quality of applicants for the positions you have already filled there? While there are other factors involved (Are the roles currently there significantly different? Were the postings placed in similar locations and written in similar ways?), this should give you a rough idea of the validity of your suggestion that is specific to your company and therefore should be convincing for your bosses (or you).
Regarding NYC in particular, there was a recent infographic about the tech scene in New York.
As someone working in NY tech I am probably biased, but I do agree with your proposition that you will find a bigger, better talent pool here. Being in the same city as Wall St is actually a plus because many developers are happy to find opportunities to apply their software skills to industries outside of finance. Also, a recent article pointed out the role that the collapse of Wall St has had in making NYC a hotspot for tech startups - high amounts of laid off workers with cash to spare and a desire to work on challenging projects has led to an increase in innovative startups and hungry talent.
So, if you are looking for a deep talent pool and are willing to invest in your people, a big city and tech hub (like NYC has become) is a great place to be.
Gazarsgo makes a really good point though - if your management is balking at the rent, will they also balk at paying competitive salaries in NYC? It's fairly easy to get salary data on the same positions in different locations, so you should also consider that as a cost of hiring in the big city. And if you want to hire better talent, what other perks will you need to provide to entice and retain them?
I think the biggest factor here is to consider how important it is to your company's vision for you to attract and retain top talent. Does your company desire to be an innovation leader, or is your software very technically complex to build? Or is your company doing something that has been done before, and wants to do it well but is ok with not pushing into cutting edge? For a company doing something that makes business sense but isn't technically very challenging or new, it may not be worth the investment required to get that deep talent that you are wanting.
Articles related to deciding to hire tech in NYC:
New York City Now Fastest-Growing Tech Hub [INFOGRAPHIC]
eBay to Open Large Tech Office in NYC
Why Has New York Become a Paradise for Tech Startups?