Custom post categories are not displaying on the page

  $args = array(
    'post_type'   => 'travelplan',
    'numberposts' => -1,
    'tax_query'   => array(
       array(
          'taxonomy' => 'travelplan_cat',
          'field' => 'slug',
          'terms' => 'testtravel'
       )
     )
   );
  $plans = get_posts( $args );

  echo '<pre>';
  print_r($plans);
  echo '</pre>';

Change your register_taxonomy like this

function create_travelPlan_taxonomy() {
    register_taxonomy(
        'travelplan_cat',
        'travelplan',
        array(
            'label' => __( 'Category' ),
            'rewrite' => array( 'slug' => 'travelplan_cat' ),
            'hierarchical' => true,
        )
    );
}
add_action( 'init', 'create_travelPlan_taxonomy');