Some gave you hints to solve your regexp problem. I will give you a quick-n-dirty non-regexp related solution (I will never put a code like this in production):

use strict;
use warnings;
use Data::Dumper;

my $i = "[[{bunches_of_data}, {more_data}, {etc}], [{hey_more_data}, {
+etc}, {etc}], [{etc}, {etc}, {etc}]]";

$i =~ s/{|}//g;
$i =~ s/([^\[\],\s]+)/'$1'/g;

my $iv = eval "$i";
print Dumper $iv;
[download]

Outputs:

$VAR1 = [
          [
            'bunches_of_data',
            'more_data',
            'etc'
          ],
          [
            'hey_more_data',
            'etc',
            'etc'
          ],
          [
            'etc',
            'etc',
            'etc'
          ]
        ];
[download]