Airtrain will only take you as far as public transportation at Howard Beach (A subway) or Jamaica (E, J subway and LIRR). The NYAS express bus to Grand Central leaves from each terminal every 20-30 minutes, cost is $15. By public transportation; take Airtrain to Jamaica Station and then E subway to Lexington Ave. Transfer there for the downtown #6 subway one stop to 42nd St./Grand Central, cost is $7.25 total. If you have alot of bags I'd take the NYAS bus, not easy to schlep on the subway.
Airtrain will only take you