Retrieve a specific post’s featured image and show on a different page

Each post object has a public member $post_parent. That is the post ID of the parent post. So this should work:

$thumbnail="";

if ( ( 'event_posts' == get_post_type()
        || is_page( 'events' )
        || is_page( 'restaurants' )
        || is_page( 'recreation' )
        || is_page( 'entertainment' )
        )
    && ! empty ( $GLOBALS['post']->post_parent )
    )
{
    $thumbnail = get_the_post_thumbnail( $GLOBALS['post']->post_parent );
}

echo $thumbnail;