Why not just check if the answer in in %menu_selection, and exit the loop only then? Something like:

while (1) {
    print <<EOF;
Please select one of the following locations:
1.) Option 1....
2.) Option 2....
3.) Option 3....

EOF
    print "Selection: ";
    chomp(my $answer = <>);
    if ($menu_selection{$answer}) {
       print $menu_selection{$answer}, "\n";
       last;
    }
}
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