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' };