Okay, regarding "which costs are potentially negotiable in closing costs," that depends upon whether the purchase is a resale or unit in a new development. In a new development, the sponsor expects the first-time buyer of the unit to pay the NYS and NYC transfer taxes. However, that can be negotiated. New developments also expect buyers to pay the sponsor's legal fees which, again, can be negotiated.
Purchase price, of course, is always negotiable, whether on a sponsor unit or a resale. Sometimes, if a co-op has a particularyly high maintenance fee or a condo has particularly high common charges, sometimes the seller might be willing to pick up 6 months or year of that. As far as beyond traditional closing costs, there may be some negotiation for leaving a particular item, such as a chandelier, or a wall unit that fits very well, but that's a little beyond the scope of your question.
Some of the closing costs can be negotiated between seller and a buyer and some can be negotiated with a lender...
Are you looking to buy in New York? I would be happy to walk you through closing costs for a specific property and identify best options for you.
646 593 7207
It is possible to negotiate all associated closing costs with the seller but I believe for that your offer should be rock solid. Good luck.