For door to door shared van service, I think allcountyexpress.com serves most of Westchester for about $40/person. A taxi will cost more, but can take more than one person.

To just get someplace close where they can pick you up, the Metro North train from Grand Central to Scarsdale is probably the way to go.

The easiest inexpensive way to get to Grand Central is the New York Airport Service bus (http://www.nyairportservice.com), which is $15/person, as described above.

Even cheaper is NYC public transit. Take the AirTrain to Jamaica ($5), then take the Manhattan-bound E train to Lexington Ave and switch to the downtown 6 train, which will take you to Grand Central ($2 total--transfers between subways are free). See our wiki for details.

The NYC public transit option is going to be difficult with luggage, though. If you have more than a single rollaboard, I'd highly recommend the bus.