You could get lucky at the town hall, they may have a copy on file. For example Lynbrook has a copy of the survey of almost every home, along with permits both open and closed. I have come accross a few homes that the owner opened up a permit for a garage, built the garage but never closed the permit (never had the work inspected). That was a problem that needed to be adjusted before the property closed. (Just as an example).
Nassau Property would be ok, but I wouldn't trust it. If the "home layout" (which is "view property sketch") Just keep in mind if the shape on the sketch doesn't match your home you have a problem.
If you cannot find your survey in an old file at home you may have to hire a company and re do the survey. (sorry) If you are thinking of puttig up a fence, make sure the surveyer places stakes. You will have to ask for the stakes, otherwise they wont do it.