Make it a weekend vacation
If I were flying some distance into the New York area I would recommend the following: Get a hotel room in Manhattan for Friday, Saturday and Sunday nights. On Friday plan to land at Republic Airport in Farmingdale, Long Island (KFRG). You can safely keep the plane their. Take the Long Island Railroad (1 hour ride) into Manhattan's Penn Station, check into your room and take in the city. Go to a Broadway show, Central Park, the Top of the Rock (Rockefellar Center), walk up Fifth Avenue, have a drink at The Plaza Hotel. Sunday morning (Game Day) go to the Bus Terminal at 8th Avenue and 42 Street and take the special "Game Day Bus" to Giants Stadium (approx. 30 minute ride). Special Bus lanes set up. You will save hours by taking the bus. Once at the stadium walk around the parking lots and introduce yourself to the tailgaters. You will be surprised how friendly and sharing they are (no kidding). After the game take the same bus back to Manhattan.
Monday morning take the railroad back to Farmingdale train station, get a cab back to KFRG and fly home.
I am sure their are other options but, as a Long Islander, this is one I know will work. Good Luck!!