The Consulate General of the Republic of Hungary in New York or the Hungarian authorities (e.g. the Ministry of Foreign Affairs or the Mayor's Offices) don't do genealogical research.
Some information on the subject may be obtained (also in English) at the homepage of the National Archives of Hungary .
You can find on the internet several companies doing genealogical research on the Hungarian site: http://genealogia.lap.hu/ or by typing in a search engine (e.g. Google, Yahoo, etc.) the keywords: Hungary genealogy.