It is hard to advise about the negotiating without knowing the price. You are in Manhattan, Midtown West based upon your zip code. You could be talking about a $4MM high floor 3-BR in the Atelier or a studio co-op in a walk-up for under $300K. My point is this might be a big or very little amount, and there are various strategies that we agents, as professional negotiators use, which take into account many factors that I don't know from your brief description. What it all really amounts to, is what the fair market value is. You seem to not have an agent and are selling on your own, which is why the negotiating is so diffiult for you. As the seller, you are emotionally involved, which is never a good position to be in. It is not a matter of how high you want him to go or how low he wants you to come as what the comps say is the true market value. Your agent, if you were listed with a professional real estate agent, would be able to advise you on that. There are other negotiating points that are just as important as purchase price. Purchse price is only one factor in the offer. I can tell you from experience that most For Sale by Owners do overprice, so your buyer may be offering you a fair price. If you are priced correctly, they may be lowballing you.
I would suggest, if you and this buyer do not reach an agreement, that you list your property with a skilled experienced agent. You will then know it is priced correctly, that it is getting the necessary exposure, and you will have a skilled negotiatior working onyour behalf. That is how to get the most money in the least amount of time. You will also not be so afraid of losing your only buyer, as you will be getting sufficient traffic to get serious buyers willing to pay market value.
Also, please do not take advice on NYC real estate from well-meaning agents who do not know our market, as there are nuances of our market that are only understood by someone who is immersed in it every day. For example, the responder below who talks about fear of "the market" falling further, we have been rising her for several quarters and are off the bottom with good inventory getting scarce. We are trending up.
Hope this helps.
Halstead Property, LLC