printf "Before deleting: city= %s state=%s zip= %s\n",
   $city ,
   $location_hash->{ $city }->{ 'ST' },
   $location_hash->{ $city }->{ 'ZIP' };

   delete ($location_hash->{ $city });
   delete ($location_hash->{ $city }->{ 'ST' }) ;
   delete ($location_hash->{ $city }->{ 'ZIP' }) ;

printf "After deleting: city= %s state=%s zip= %s\n",
   $city,
   $location_hash->{ $city }->{ 'ST' },
   $location_hash->{ $city }->{ 'ZIP' };

##</code><code>##

Before deleting: city= Lucketts state=VA zip= 20176
After deleting: city= Lucketts state= zip=

##</code><code>##

for my $city ( keys %$location_hash ) {
   .
   .
   .

   printf "Before deleting: state=%s zip= %s\n",
      $location_hash->{ $city }->{ 'ST' },
      $location_hash->{ $city }->{ 'ZIP' };

   delete ($location_hash->{ $city });
   ### delete ($location_hash->{ $city }->{ 'ST' }) ;
   ### delete ($location_hash->{ $city }->{ 'ZIP' }) ;

   printf "After deleting: state=%s zip= %s\n",
      $location_hash->{ $city }->{ 'ST' },
      $location_hash->{ $city }->{ 'ZIP' };

} end for loop

##</code><code>##

Before deleting: state=VA zip= 20176
After deleting: state= zip=
Before deleting: state=VA zip= 20176
After deleting: state= zip=