Travel Note
Syracuse, NY is the easy answer. It is about a 2 hour drive from Elmira. Some other airports worth noting are Wilkes-Barre, PA (also about 2 hours), and Buffalo, NY (about 2.5hrs). Ithaca, NY (45min) and Elmira, NY also have airports but they are very small and may cost more.
Travel Note
We would recommend staying in Horseheads, NY if you are looking for somewhere close to where we live. Other places to consider are Corning, Watkins Glen, Ithaca, or Sayre, PA.