There is a shuttle called AirLink that runs from the airport to the White Plains train station. The schedule is here:
http://www.westchestergov.com/beelin...ge/airlink.pdf
From White Plains train station it's about 35 minutes to Grand Central (less to Harlem-125th St) if you catch an express train.
If your flight is too early or late though the shuttle doesn't run all hours, so you'll have to take a cab, which is pretty expensive and might make it just as expensive as flying into LaGuardia anyway.