If you have a data structure and don't know what's in there, use Data::Dumper to dump it:

use Data::Dumper;
my $content = join '', <DATA>;
my $response = XMLin($content);
print Dumper($response);
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This will print something like

$VAR1 = {
  'offer' => {
    '6' => {
      'zip' => '48120',
      'transit' => '1',
      'smoking' => {},
      'phone_public' => '1',
      'state' => 'MI'
    },
    '60046' => {
      'zip' => '80236',
      'transit' => '1',
      'smoking' => {},
      'phone_public' => '1',
      'state' => 'CO'
    },
    '7' => {
      'zip' => '43240',
      'transit' => '1',
      'smoking' => {},
      'phone_public' => '1',
      'state' => 'MI'
    }
  }
};
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and shows that starting from $response (which is a reference to a hash), you need to step down to the value of the offer key.

There, you'll find another reference to a hash. This one contains one entry per id, so all you need to do is loop over these keys and then step down to the zip element of the sub-hash:

my $response = XMLin($content);

for my $id (keys %{$response->{offer}}) {
    print $response->{offer}->{$id}->{zip}, "\n";
}
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This will print the zip codes you're interested in:

48120
80236
43240
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