Keep in mind all New York state counties have varying times you can buy alcohol. But for the basis of NYS law here is the rundown of Alcohol laws in New York:
For off-premise consumption, between 3–6 a.m. any day of the week, other than Sunday, as beer sales are prohibited from 3–8 a.m. Sundays. Counties are free to adjust those hours in either direction, all the way to midnight and noon, and allow 24-hour beer sales on other days of the week.
For on-premise consumptions (i.e. bars, restaurants), you cannot buy alcohol between 4:00 a.m. and 8:00 a.m. in New York state each day of the week .
"This was designed to accommodate New York City nightlife as well as late night workers statewide in general. Some upstate areas such as Buffalo, Albany, and Saratoga Springs retain the 4am closing time although individual counties are free to set an earlier "last call." In Binghamton, this is at 3:00 a.m., in Syracuse, Plattsburgh, Oneonta, and Rochester, bars close at 2:00 a.m., and Elmira, Geneva, and Ithaca, have some of the earliest closing times in the state at 1 a.m. In some counties, Alcohol may not be served before 12 Noon on Sunday. For a complete list closing hours by county, see http://www.sla.ny.gov/provisions-for-county-closing-hours."
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See individual county closing hours for Liquor, Wine and Beer here: http://www.sla.ny.gov/provisions-for-county-closing-hours