Making a Custom Post Type Plugin – keep getting the white screen of death

You are closing your function right after the $args array. You need to enclose properly

function local_business_directory_register() { 

$args = array( 
  'label' => __('Business Directory'), 
  'singular_label' => __('Business'), 
  'public' => true, 
  'taxonomies' => array('category'),
  'show_ui' => true, 
  'capability_type' => 'post', 
  'hierarchical' => true, 
  'has_archive' => true,
  'supports' => array('title', 'editor', ),
  'rewrite' => array('slug' => 'businesses', 'with_front' => false),
  ); 

  register_post_type( 'businesses' , $args );
  register_taxonomy("business-type", array("businesses"), array(
  "hierarchical" => true,
  "label" => "Business Type",
  "singular_label" => "Business Type",
  "rewrite" => true
     )
    );

}