Batavia, NY has a "general aviation" or private aircraft airport of its own, but for large scale commercial service you would look to either Rochester (ROC) or Buffalo (BUF). These are about 30 to 40 miles or a 45 to 60 minute drive in good weather.
Within several hours there are other regional and major airports including Syracuse, Ithaca, and Binghamton, plus Erie and Pittsburgh PA, Cleveland OH, and Toronto Canada. You might consider these for possibly lower fares, travel conditions, or points of interest.
The closest major airport to Swan Lake, New York is Stewart International Airport (SWF / KSWF). This airport is in Newburgh, New York and is about 52 miles by car from the center of Swan Lake, NY.
LaGuardia Airport (LGA / KLGA), New York.
Albany
La guardia
The nearest major airport is Greater Binghamton Airport(BGM / KBGM). This airport has domestic flights from Binghamton, New York and is about 46 road miles from the center of Norwich, NY.
Since the NY Giants play at the Meadowlands in East Rutherford, NJ, Newark International Airport is closest.
The closest major airport to Rochester, New York is Greater Rochester International Airport (ROC / KROC). This airport is about 4 miles from the center of Rochester.
The cast of New York - Batavia - 1989 includes: Dolf de Vries as Voice of man
The nearest major airport is Westchester County Airport(HPN / KHPN). This airport has international and domestic flights from White Plains, New York and is about 25 road miles from the center of Bardonia, NY.
The nearest major airport is Elmira/Corning Regional Airport (ELM / KELM). This airport has domestic flights from Elmira, New York.
LaGuardia Airport is the closest. LaGuardia is written as if it's one word because it's an Italian last name and someone wrote it himself*. LaGuardia Airport and LaGuardia Community College in New York are both named after former New York Governor Fiorello H. LaGuardia.
The nearest major airport is Westchester County Airport(HPN / KHPN). This airport has international and domestic flights from White Plains, New York and is about 25 miles by car from the center of Spring Valley, NY.