I think you want to use chdir to change into the directory you want.
Using opendir, you can do like so:

use warnings;
use strict;

print "Enter a directory:";
chomp( my $dir = <STDIN> );

print "String looked for: ";
chomp( my $str = <STDIN> );

chdir $dir or die $!;

opendir DH, $dir or die $!;
while ( readdir(DH) ) {
    next if $_ eq '.' or $_ eq '..';
    unless (-d) {
        open my $fh, '<', $_ or die $!;
        while (<$fh>) {
            print $_ if /\Q$str/;
            last;
        }
    }
}
closedir DH or die $!;
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