I suggest using Path::Tiny for working with the files: its visit method can recursively walk a directory tree and apply a subroutine to each filename found, accumulating a list of matching files. The solution to matching the filenames will depend on the naming format used.

Update: since you showed the format elsewhere ... try something like this:

use strict;
use warnings;
use feature 'say';
use Data::Dumper;
use Path::Tiny;
use Time::Piece;

my $root = "/Users/1nickt/perlmonks/11133966";
my $today = localtime->strftime('%Y%m%d');
my %list;

path($root)->visit(sub {
    my $path = shift;
    next unless -d $path;
    my $date = substr($path, -8);

    if ( $date =~ /^[0-9]{4}[0-2][0-9][0-3][0-9]$/ && $date gt $today 
+) {
        push(@{ $list{$_->parent} }, $path =~ s{.+/}{}r);
    }
}, {
    recurse => 1,
});

say Dumper \%list;
[download]

Hope this helps!