1. Visit >Settings>Custom fields and add to section "Customer fields" following text ( edit list for your needs)


City|city|select|CityName1|CityName2|CityName3|CityName4


2. Add following PHPcode to functions.php

add_action( "wpo_set_cart_customer", function ( $cart_customer, $id, $customer_data ) {
  /* @var WC_Customer $cart_customer
  */
  if ( $cart_customer->meta_exists( 'city' ) ) {
    $city_code = $cart_customer->get_meta( 'city' );
    $cart_customer->set_billing_city( $city_code );
    $cart_customer->set_shipping_city( $city_code );
    $cart_customer->apply_changes();
  }
}, 10, 3 );