Topher

This plugin provides a metabox on posts and pages listing existing WordPress Menus. The end user is allowed to choose one and make it associated with the post or page via meta data.
Practically speaking, Featured Menus work exactly like Featured Images. The Post or Page and Featured Menu are merely attached, and you must use a template tag or WordPress functions to render the Menu.
Please see <a href="https://wordpress.org/plugins/wp-featured-menus/other_notes/" rel="ugc">Other Notes</a> for examples.
<h3>Usage</h3>
Page or Post meta has a key called <code>_wp_featured_menu</code>. A very simple way to render the menu is like this:
<pre><code><?php
 $meta = get_post_custom();
 wp_nav_menu( array( 'menu' => $meta['_wp_featured_menu'][0] ) );
?>
</code></pre>
A better way might be to test for the value first:
<pre><code><?php
 $meta = get_post_custom();
 if ( is_numeric( $meta['_wp_featured_menu'][0] ) ) {
 wp_nav_menu( array( 'menu' => $meta['_wp_featured_menu'][0] ) );
 }
?>
</code></pre>

WP Featured Menus

Provides a metabox on posts and pages listing existing WordPress Menus.

Austin

Fulvio Notarstefano

This plugin extends the <a href="https://wordpress.org/plugins/json-rest-api/" rel="ugc">WordPress JSON REST API</a> with new routes for WordPress registered menus
The new routes available will be:
<ul>
<li><code>/menus</code> list of every registered menu.</li>
<li><code>/menus/<id></code> data for a specific menu.</li>
<li><code>/menu-locations</code> list of all registered theme locations.</li>
<li><code>/menu-locations/<location></code> data for menu in specified menu in theme location.</li>
</ul>
Currently, the <code>menu-locations/<location></code> route for individual menus will return a tree with full menu hierarchy, with correct menu item order and listing children for each menu item. The <code>menus/<id></code> route will output menu details and a flat array of menu items. Item order or if each item has a parent will be indicated in each item attributes, but this route won’t output items as a tree.
You can alter the data arrangement of each individual menu items and children using the filter hook <code>json_menus_format_menu_item</code>.
An important note on WP API V2:
In V1 the routes are located by default at <code>wp-json/menus/</code> etc.
In V2 the routes by default are at <code>wp-json/wp-api-menus/v2/</code> (e.g. <code>wp-json/wp-api-menus/v2/menus/</code>, etc.) since V2 encourages prefixing and version namespacing.

WP API Menus

It Does!

Extends WordPress WP REST API with new routes pointing to WordPress menus.

WP Featured Menus vs WP API Menus