Here's a hybrid solution. I'm inclined to agree that join(grep(split())) is going to be more robust, but this might be more economical:

$_ = '/New York/Chicago/New York/Boston/Houston/Chicago/Seattle/';
my %tally;
s/\/([^\/]+)/($tally{$1}++) ? '' : "\/$1"/ge;
print $_;

__END__
prints /New York/Chicago/Boston/Houston/Washington/
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Note that this requires a leading / if it's to remove duplicates of the first item in the list. Split handles that sort of thing better...