To remove WooCommerce checkout fields like billing address without a WordPress plugin, add the following code to your themes functions.php file.
/* Removes WooCommerce Billing and order comments Checkout Fields code */
add_filter( 'woocommerce_checkout_fields' , 'custom_remove_checkout_fields_blogies' );
function custom_remove_checkout_fields_blogies( $fields ) {
unset($fields['billing']['billing_company']);
unset($fields['billing']['billing_address_1']);
unset($fields['billing']['billing_address_2']);
unset($fields['billing']['billing_city']);
unset($fields['billing']['billing_postcode']);
unset($fields['billing']['billing_country']);
unset($fields['billing']['billing_state']);
unset($fields['order']['order_comments']);
return $fields;
}