From my experience, the best way to get to valhalla is to take the train from Grand Central Station, which is located right in the middle of New York, to valhalla. The train could also be taken to White Plains, which is about a ten minute drive from valhalla, since White Plains is a bigger station and has more trains. good luck!
It is actually better to fly into Westchester County Airport, and catch a cab from there to the school because it's not that far. The only problem is that flights to that airport cost more than flights that arrive at larger airports like JFK or La guardia. I would avoid newark at all cost. Your best bet would be JFK becuase you can take the air train to Howard Beach and catch a train from there.
It depends upon your budget. When I interviewed my plane was getting in kind of late, so my dad gave me money for a shuttle that took me to Valhalla (had to change shuttles at a hotel in White Plains). On my way back I had time, so I took a cab to the WP train station, the train to Grand Central, and then the bus from Grand Central to the airport. The buses can get you to any airport. Also, there is an airport in White Plains. Everyone says it's expensive, but I have found some good flights in and out of it. Good luck!!!