You have already discovered that you need the EXPR (not BLOCK) form of eval. With this change, your original idea of removing $VAR1 works fine.

use strict;
use warnings;
use Data::Dumper qw(Dumper);
my $hash;
{
    local $/;
    $hash = <DATA>;
}
#$hash = eval { $hash };
 $hash = eval   $hash  ;
 print keys %$hash; # error   (no more)

  __DATA__
  #$VAR1 = {
           {
            'blah.com' => [
                                               '212.235.56.176'
                                             ],
            'blah.org' => [
                                  '212.235.56.176'
                                ],
            'www.boo.org' => [
                                 '212.235.56.176'
                               ],
};
[download]

OUTPUT:

C:\Users\Bill\forums\monks>perl 11116141.pl
blah.comblah.orgwww.boo.org
[download]