newark airport (ewr) has its own amtrak stop on the northeast corridor, with frequent service from new haven. if you book your amtrak ticket when you book your plane ticket, you can get there directly for fairly cheap ($20-ish) from union station in new haven. from the ewr stop, you just take the airtrain tram to your terminal.

it's the easiest transit-to-airport connection in the area, although the windsor locks option to bradley is workable and so are the queens airports.