OK, that is from the entity that makes the decision of substance, yes.
You will NOT be visiting the Binghamton office, no. They don't entertain visitors. I am a bit closer to Binghamton than you, where the ODAR hearings are. You can ALWAYS drop papers off at a field office closer to you. Note that SSA offices (field offices) do not adjudicate. There are only there to collect mail and send claims off to the next level where it can be adjudicated.
Again, if you have a person's NAME in the NY adjudication office, you can call him/her - usually there will be the general phone number PLUS his/her extension. I have nothing special to note about this office, no. They are what they are.
But again, its location is irrelevent, since that is not a place you visit - you just send additional evidence to your adjudicator, should you have any. When you appeal for a hearing, that is when it will be closer to your home. You put all your evidence, or correspondence, in writing to the adjudicator, if possible - even if you leave him a message or get him on the phone - confirmable mailing is a good idea.
And yes, your local field office is simply a clerical receptacle to recieve claims, there are no adjudicators there. In fact, despite directions to contrary, we don't even send medical evidence there when we do not yet KNOW the name and contact info for the adjudicator - this is because 50% of the time the evidence never gets connected to the file and the adjudicator never sees it. Rather, once we know there is an adjudicator, we call him or his office if that is all we can reach, and ask for a BAR CODE PAGE and corresponding FAX number to which we may fax the paperwork (if we don't want to send it UPS) - the bar code is unique to your/your case and best ensures your evidence ends up in your digital file.
I hope this helps! My goal is to provide you with excellent and accurate service – if you feel you have gotten anything less, please reply back, I am happy to address follow-up questions. Kindly rate me "excellent" when you are done. I look forward to assisting you in the future, should you have legal questions.