Remove zipcode field and add custom dropdown in its place.

custom_dropdown.php

<?php

// Lets remove the postcode
add_filter( 'woocommerce_checkout_fields' , 'custom_wc_checkout_fields' );
function custom_wc_checkout_fields( $fields ) {

	unset( $fields['billing']['billing_postcode']);

	$fields['billing']['shipping_code'] = array(
		'type'          => 'select',
		'class'         => array( 'shipping-code' ),
		'label'         => __( 'Shipping Code' ),
		'required'      => true,
		'priority'       => '80',
		'options'       => array(
			''		        => __( 'Select an area ', 'mt' ), // Displays as placeholder and is not selectable
			'value for option 1'	=> __( 'Option 1'       , 'mt' ), // Update value for value. Change Option 1 for text to display.
			'value for option 2'	=> __( 'Option 2'       , 'mt' ),
			'value for option 3' 	=> __( 'Option 3'       , 'mt' )
		)
	);

	return $fields;

}

// Add custom field to order meta
add_action( 'woocommerce_checkout_update_order_meta', 'custom_select_checkout_field_update_order_meta' );
function custom_select_checkout_field_update_order_meta( $order_id ) {

	if ( $_POST['shipping_code']) {

		update_post_meta( $order_id, 'shipping_code', esc_attr($_POST['shipping_code']));

	}

}

// Add to admin order area
add_action( 'woocommerce_admin_order_data_after_billing_address', 'add_custom_select_checkout_field_display_admin_order_meta', 10, 1 );
function add_custom_select_checkout_field_display_admin_order_meta($order){

	echo '<p><strong>'.__('Shipping Code').':</strong><br> ' . get_post_meta( $order->id, 'shipping_code', true ) . '</p>';

}

// Add field value to emails
add_filter('woocommerce_email_order_meta_keys', 'custom_select_order_meta_keys');
function custom_select_order_meta_keys( $keys ) {

	$keys['Shipping Code'] = 'shipping_code';

	return $keys;

}

// Adds shipping code after Order details on Thank you page and my account > order page
add_action('woocommerce_order_details_after_order_table', 'action_woocommerce_order_details_after_customer_details', 10, 1);
function action_woocommerce_order_details_after_customer_details($order) {

	echo '<p><strong>'.__('Shipping Code').':</strong><br> ' . get_post_meta( $order->id, 'shipping_code', true ) . '</p>';

}