B737-300 FLC ACCEPTS CHARTED VISUAL APCH TO LGA WITHOUT IDENTING PROPER LANDMARK.

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IT WAS MY FIRST MONTH ON THE LINE AS A B737-300 FO AND I HAD NEVER BEEN INTO LGA ARPT. WE DEPARTED ORD AND IT WAS THE CAPT'S LEG. WE HAD BRIEFED AN ILS TO RWY 13; BUT WERE TOLD DSNDING TO 5000 FT MSL TO EXPECT A VISUAL APCH. LEVELING OFF AT 5000 FT MSL WHILE ON VECTORS; APCH ASKED US IF WE HAD THE 'LADY;' REFING THE STATUE OF LIBERTY. I DID NOT HAVE IT IN SIGHT; BUT THE CAPT SAID HE DID; SO I RPTED THAT WE HAD THE LADY IN SIGHT. THE CAPT POINTED TO WHAT HE THOUGHT WAS THE LOCATION OF THE STATUE. MEANWHILE APCH CLRED US FOR THE RIVER VISUAL WHICH WE HAD NEVER PREBRIEFED AND WHICH I HAD NEVER SEEN. THE CAPT TOOK A 30 DEG R TURN TO HEAD FOR IT. ABOUT 10 SECONDS LATER; APCH CALLED US AND TOLD US TO TURN 40 DEGS TO OUR L IMMEDIATELY; AND ASKED US IF WE HAD THE LADY. THE CAPT SAID HE HAD THE HUDSON BRIDGE; AND WE WERE CLRED TO 4000 FT MSL TO FOLLOW THE RIVER VISUAL. LANDED UNEVENTFULLY. WE SAW THE STATUE SOON AFTER SPOTTING THE HUDSON BRIDGE. PULL OUT THE PROC -- THE RIVER VISUAL APCH GRAPHICALLY DESCRIBES WHERE EVERY LANDMARK IS LOCATED. BRIEF ADDITIONAL APCHS -- ESPECIALLY IF YOU'VE NEVER BEEN THERE BEFORE.