Buffalo (/ˈbʌfəloʊ/) is a city in Western New York and the seat of Erie County, located on the eastern shores of Lake Erie at the head of the Niagara River.uffalo is home to three State University of New York (SUNY) institutions. The University at Buffalo and Buffalo State College are the largest institutions of their type in the system. The total enrollment of these 3 SUNY institutions combined is approximately 54,000 students in the area.