I'm from right around westchester medical center (my stepmom works there), and i live in cali. Getting from JFK or LaGuardia to westchester is a bit of a pain in the butt if you don't have parents to schlep you, so flying into white plains airport would be the best solution. Sometimes, it can even be the cheapest option (granted, you will need to connect in minnesota or chicago most likely). White Plains airport is nearby (you could probably arrange for a student to pick you up or take a cab) and it is very very small.
Otherwise, as the previous post said, from JFK you take the new sky train which connects to the NYC subways, and take those to grand central. the harlem line gets you to valhalla in ~40minutes 🙂