Instead of

> my $wanted_regex = qr/B/;

> ... grep $wanted_regex, @cities;

please try

• grep /$wanted_regex/, @cities;

or

• grep { $_ =~ $wanted_regex } @cities;

or

• variations of aforementioned

Explanation:

$wanted_regex is a variable holding an Regexp object (at runtime) not an operator.

And objects resp. their references are always true, that's why you get the whole list.

You need to specify at least one operator for the parser to know what you really want.

update

tested code and expanded explanation