Gail is absolutely right. I would only add the following:
New York State is the only state in the Union that charges its resident a tax for taking out a mortgage, which I believe is approximately 1.875% of the loan amount.
The lender you choose will have an impact on the total cost for closing your purchase.
MY ADVICE: Interview direct lenders and large mortgage banks in the city to see what they are charging your to underwrite your loan (points) and what costs are they willing to absorb (appraisal, notary fees, survey, etc...)