perluniintro shows a function nice_string() which essentially does what you want (i.e. render special characters as \x... escapes), and can easily be adapted to your likings.  For example, here in slightly modified form:

#!/usr/local/bin/perl -l

sub nice_string {
    join(" ",
      map { $_ > 255 ?                  # if wide character...
            sprintf("\\x{%04X}", $_) :  # \x{...}
            chr($_) =~ /[[:cntrl:]]/ ?  # else if control character ..
+.
            sprintf("\\x%02X", $_) :    # \x..
            chr($_)                     # else as themselves
      } unpack("U*", $_[0]));           # unpack Unicode characters
}

my $var = "Some random text.\nMore\nEven More\n";
print nice_string($var);

__END__
S o m e   r a n d o m   t e x t . \x0A M o r e \x0A E v e n   M o r e 
+\x0A
[download]

(It expects a decoded character string.)