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for (values %$HASH1) {
    my %seen;
    $_ = [ grep { ! $seen{$_}++ } @$_ ];
}

my %seen;
for (values %$HASH1) {
    $_ = [ grep { ! $seen{$_}++ } @$_ ];
}

my %seen;
$_ = [ grep { ! $seen{$_}++ } @$_ ] for values %$HASH1;

{
  "Alabama"    => ["Andalusia", "Anniston", "Clanton", "Eufaula", "Aub
+urn"],
...
  "New York"   => ["Amsterdam", "Coney Island", "Beacon"],
  "Utah"       => ["Layton"],
}

$_ = [ grep { state %seen; ! $seen{$_}++ } @$_ ] for values %$HASH1;