metro north only goes as far as new haven. there is an amtrak train that goes from new haven to hartford, but only a few times a day, so check the schedules. It's probably easiest to take amtrak directly from new york - also becuase metro north leaves from grand central while amtrak leaves from Penn station, and the trains you would get from JFK (A, E, or LIRR) all go to Penn station and not grand central.
metro north only goes as far