Actually, the Passaic River Runs right by the Arena, in fact there are several private boatclubs located just behind the arena, I'm not sure if their technically in East Rutherford, Carlstadt or Moonachie.
Although fish and crabs are caught there, I don't think there are many accessable places and besides, the water is a bit dicey there.
Best bets would be Hoboken near Frank Sinatra Park on River Road and Grundy Pier in JC. Other options might be Hudson River Park and Battery Park in Manahatten.
I recommend taking a drive to fish on Raritan Bay.
Floyd Bennet Field Brooklyn, Great Kills Harbor in Staten Island or Sandy Hook in NJ are all part of Gateway National Park. There are also many places in Monmouth County along the Raritan between Staten Island and Sandy Hook (Belford Beach for example). If you check the Hot Spots link you'll find Keyport, Spy House and Keansburg Piers listed, this is the area I'm talking about.
All of the above are within 1 Hour of the Meadowlands (sans traffic) Sandy hook is about the farthest. It's about 55 miles or so from the Meadowlands.