It is feasible to get to Fairfield on public transport. What your boyfriend would need to do is take the subway to Manhattan to Penn Station. Then, he would take the NJTransit train from Penn to Newark Penn Station. From there, he would need to take Bus 29 to West Caldwell. From West Caldwell, it would be Bus 71 towards Fairfield, which goes right by the Essex County Airport from the bus map. Due to scheduling delays and such, it could actually take close to two hours door-to-door with all of the connections, two trains and two buses plus overlap wait times. If he really wants to do it, though, check the schedules and see if the airport can offer any faster means of getting there.
Here's a link to NJTransit for more information:
New Jersey Transit