my @test_centers_sorted_by_city_then_name = sort { $centercity{$a} cmp $centercity{$b} || $a cmp $b } keys %centercity;

for my $center (@test_centers_sorted_by_city_then_name) {
   print "$center<br>";               # output test center name
   print "$centercity{$center}<br>";  # output city where test center is located
   # ... output other stuff too
}