BataviaThrills.com! . . . Batavia, NY is the birth place of Western New York... Population as of 2000: 16,256... In 1802, Joseph Ellicott purchased 3.5 million acres in Western New York... The average winter temperature in Batavia is 23.5 degrees farenheit...The all time high temperature was 98 degrees farenheit...The greatest one-day snowfall was 23 inches.