んなら、ユニコードでも使ってみようか。

use Encode;

my $pattern = '([A-Z0-9]+号室)';
my $str = "1階206号室";
Encode::from_to($pattern, 'sjis', 'utf8');
Encode::from_to($str, 'sjis', 'utf8');
$str =~ /$pattern/;
my $match = $1;
Encode::from_to($match, 'utf8', 'sjis');
print $match;