BubbaMax,
Very nice finds! You have found two interesting National Geodetic Survey disk. Here is some info on them. The disk at the VFW was placed there way back in 1961. Back then it was the Coast and Geodetic Survey (CGS). The disk is named K 57 and it is important to know it is not K57. There has to be a space between them making it K 57. The actual datasheet on that disk is below.
The disk your dad took you to has a little history to it. It isn’t the first disk to be there. The first one was placed there in 1961 but in 1964 a local surveyor (LOCSUR) found it to be missing. So he did a “Reset” which means he placed a new one there, so now it is called F 57 Reset 1964. Again, there is a space between the F and the 57.  And also below is the info on the first F 57 and the Reset that you photographed.
If you have any other questions or find some more, by all means write back and I will give you all the info I can on it. 
Happy Hunting!
Guy
The NGS Data Sheet
   ***********************************************************************
    DESIGNATION -  K 57
    PID         -   
    STATE/COUNTY-  NJ/ATLANTIC
    USGS QUAD   -  MAYS LANDING (1989)
  
                           *CURRENT SURVEY CONTROL
    ___________________________________________________________________
  * NAD 83(1986)-  39 27 42.     (N)    074 43 21.     (W)     SCALED    
  * NAVD 88     -         6.300  (meters)      20.67   (feet)  ADJUSTED  
    ___________________________________________________________________
      .The horizontal coordinates were scaled from a topographic map and have
  .an estimated accuracy of +/- 6 seconds.
  
    _MARKER: DB = BENCH MARK DISK
  _SETTING: 34 = SET IN THE FOOTINGS OF SMALL/MEDIUM STRUCTURES
  _SP_SET: CONCRETE FOOTING OF FLAGPOLE
  _STAMPING: K 57 1961
  _MARK LOGO: CGS   
  _STABILITY: C = MAY HOLD, BUT OF TYPE COMMONLY SUBJECT TO
  +STABILITY: SURFACE MOTION
  _SATELLITE: THE SITE LOCATION WAS REPORTED AS NOT SUITABLE FOR
  +SATELLITE: SATELLITE OBSERVATIONS - July 13, 1990
  
    HISTORY     - Date     Condition        Report By
    HISTORY     - 1961     MONUMENTED       CGS
    HISTORY     - 19900713 GOOD             NJGS
    HISTORY     - 20040708 GOOD             GEOCAC
  
                            STATION DESCRIPTION
  
  'DESCRIBED BY COAST AND GEODETIC SURVEY 1961
  '0.4 MI NE FROM MAYS LANDING.
  '0.45 MILES NORTHEAST ALONG U.S. HIGHWAY 50 FROM THE POST OFFICE
  'IN MAYS LANDING.  MARK IS 62 FEET SOUTH OF THE EAST CORNER OF
  'V.F.W. BUILDING, 98 FEET NORTHWEST OF THE CENTER LINE OF HIGHWAY
  '50, AND IT IS SET HORIZONTALLY 1 FOOT ABOVE GROUND IN THE EAST
  'CORNER OF A CONCRETE FOUNDATION (4 1/2 BY 5 1/2 FEET) OF FLAGPOLE
  'AT V.F.W. POST NORTHEAST OF MAYS LANDING.
  
                            STATION RECOVERY (1990)
  
  'RECOVERY NOTE BY NEW JERSEY GEODETIC SURVEY 1990
  'THE STATION IS LOCATED IN HAMILTON TOWNSHIP, SET IN THE SOUTHEAST
  'CORNER OF THE FLAG POLE FOUNDATION OF THE MAYS LANDING VFW POST 220
  'COMPLEX.  TO REACH THE STATION FROM THE NORTH JUNCTION OF STATE ROUTE
  '50 AND U.S. HIGHWAY 40, GO 1.28 KM (0.80 MI) NORTH NORTHEAST ON ROUTE
  '50 TO THE STATION ON THE LEFT, ALSO 1.84 KM (1.14 MI) SOUTH SOUTHWEST
  'FROM THE JUNCTION OF STATE ROUTE 50 AND U.S.HIGHWAY 322 TO THE
  'STATION ON THE RIGHT, 0.9 M (3.0 FT) SOUTHEAST OF THE FLAG POLE, 18.9
  'M (62.0 FT) SOUTHWEST OF THE EAST CORNER OF THE ONE STORY BRICK
  'BUILDING, 23.25 M (76.28 FT) EAST OF THE SOUTH CORNER OF THE SAME
  'BUILDING AND LEVEL WITH THE GROUND.
  
                            STATION RECOVERY (2004)
  
  'RECOVERY NOTE BY GEOCACHING 2004 (STC)
  'HANDHELD GPS COORDINATES N 39 27 44.1  W 074 43 20.7
  
The NGS Data Sheet
    ***********************************************************************
     DESIGNATION -  F 57 RESET 1964
     PID         -    
     STATE/COUNTY-  NJ/ATLANTIC
     USGS QUAD   -  EGG HARBOR CITY (1977)
   
                            *CURRENT SURVEY CONTROL
     ___________________________________________________________________
   * NAD 83(1986)-  39 30 23.     (N)    074 40 39.     (W)     SCALED    
   * NAVD 88     -        17.36   (meters)      57.0    (feet)  RESET     
     ___________________________________________________________________
      .The horizontal coordinates were scaled from a topographic map and have
   .an estimated accuracy of +/- 6 seconds.
   
     _U.S. NATIONAL GRID SPATIAL ADDRESS: 18SWJ277730(NAD 83)
   _MARKER: DB = BENCH MARK DISK
   _SETTING: 30 = SET IN A LIGHT STRUCTURE
   _SP_SET: CULVERT
   _STAMPING: F 57 RESET 1964
   _STABILITY: D = MARK OF QUESTIONABLE OR UNKNOWN STABILITY
   _SATELLITE: THE SITE LOCATION WAS REPORTED AS NOT SUITABLE FOR
   +SATELLITE: SATELLITE OBSERVATIONS - September 25, 2004
   
     HISTORY     - Date     Condition        Report By
     HISTORY     - 1964     MONUMENTED       LOCSUR
     HISTORY     - 20040925 GOOD             GEOCAC
   
                             STATION DESCRIPTION
   
   'DESCRIBED BY LOCAL SURVEYOR (INDIVIDUAL OR FIRM) 1964
   '2.2 MI SW FROM EGG HARBOR CITY.
   '2.25 MILES SOUTHWEST ALONG U.S. HIGHWAY 50 FROM THE POST OFFICE
   'IN EGG HARBOR CITY, 52.50 FEET WEST OF THE CENTERLINE OF THE
   'SOUTHBOUND LANE OF U.S. HIGHWAY 50 AND SET HORIZONTALLY
   '30 1/2 INCHES BELOW HIGHWAY IN THE MIDDLE OF THE WEST CONCRETE
   'HEADWALL OF TWO 36 INCHES PIPE CULVERT.  THE CULVERT IS 80.3
   'FEET SOUTH OF THE SOUTHWEST PIER OF THE BRIDGE CARRYING THE
   'ATLANTIC CITY EXPRESSWAY OVER U.S. HIGHWAY 50.
   
                             STATION RECOVERY (2004)
   
   'RECOVERY NOTE BY GEOCACHING 2004 (STC)
   'DISTANCE FROM EGG HARBOR CITY POST OFFICE TO STATION IS 2.5 MILES.
   'HANDHELD GPS COORDINATES N 39 30 23.9 W 074 40 38.7.
The NGS Data Sheet
   ***********************************************************************
    DESIGNATION -  F 57
    PID         -   
    STATE/COUNTY-  NJ/ATLANTIC
    USGS QUAD   -  EGG HARBOR CITY (1977)
  
                           *CURRENT SURVEY CONTROL
    ___________________________________________________________________
  * NAD 83(1986)-  39 30 23.     (N)    074 40 39.     (W)     SCALED    
  * NAVD 88     -        17.933  (meters)      58.84   (feet)  ADJUSTED  
    ___________________________________________________________________
    _U.S. NATIONAL GRID SPATIAL ADDRESS: 18SWJ277730(NAD 83)
  _MARKER: DB = BENCH MARK DISK
  _SETTING: 30 = SET IN A LIGHT STRUCTURE
  _SP_SET: CULVERT
  _STAMPING: F 57 1961
  _STABILITY: D = MARK OF QUESTIONABLE OR UNKNOWN STABILITY
  
    HISTORY     - Date     Condition        Report By
    HISTORY     - 1961     MONUMENTED       CGS
    HISTORY     - 19640709 MARK NOT FOUND   LOCSUR
  
                            STATION DESCRIPTION
  
  'DESCRIBED BY COAST AND GEODETIC SURVEY 1961
  '2.2 MI SW FROM EGG HARBOR CITY.
  '2.25 MILES SOUTHWEST ALONG U.S. HIGHWAY 50 FROM POST OFFICE IN
  'EGG HARBOR CITY AND 0.95 MILES SOUTHWEST OF E 57.  MARK IS 23
  'FEET NORTHWEST OF THE CENTER LINE OF THE HIGHWAY CLOSE TO POWER
  'LINE POLE NUMBER ACE 3547.  IT IS SET HORIZONTALLY 6 INCHES
  'ABOVE HIGHWAY IN THE NORTHEAST END OF THE NORTHWEST CONCRETE
  'HEAD WALL OF AN 18 INCH PIPE CULVERT ON U.S. HIGHWAY 50.
  
                            STATION RECOVERY (1964)
  
  'RECOVERY NOTE BY LOCAL SURVEYOR (INDIVIDUAL OR FIRM) 1964
  'MARK NOT FOUND.