Some additional thoughts...

# Since you are pre-defining the cities, you don't really need the spl
+it.
# Simply pre-populate an array
my $myCities = "Baltimore:Chicago:Los Angeles:New York:San Diego:";
my @myCities = split(':', $myCities);

print "Please pick one of the following cities by entering any portion
+ of the beginning of the city 
+name:(Baltimore Chicago Los Angeles New York San Diego)\n";
# Use the above array to populate the names. That way you don't have t
+o do it twice.

chomp (my $input_city = <STDIN> );

# Take a look at 'for' and '$_' for the loop
foreach $city (@myCities) {

    # As has been noted, use 'eq' (strings) instead of '==' (numbers)
    # Better still, use a regular expression to be able to match 1 or 
+more letters
    # and, if all you want is the print output, take a look at 'unless
+'

    if ( $input_city == $myCities )  {
        #exists;  
    } else {
        print "I'm sorry,we no longer tour LA, please try again.\n";
    }
}
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