Update: The location of the perl script is available in $O. To get its directory, use dirname from the File::Basename module:

use File::Basename qw(dirname);
my $script_dir = dirname($0);
my $path = "$script_dir/Pandoras Box/$file.txt";
...
[download]

Original response:

The current working directory can always be referred to as . (a single dot), so there is no need to call the cwd command. It appears that you are just trying to do this:

chomp(my $file =uc(<STDIN>));
my $path = "./Pandoras Box/$file.txt";
open FILE, '>>', $path or die "unable to append to $path: $!";
...
[download]

Note that the append mode designator '>>' comes before the path name (preferably as a separate argument), and I can't think of why you would need double forward slashes.

Indeed, in this case specifing the current working directory with . is not even necessary:

my $path = "Pandoras Box/$file.txt";
...
[download]