shoutarou975

Restaurant Menu Japan provides:
<ul>
<li>Custom Post Type <code>wrmj_menu_item</code> and taxonomy <code>wrmj_menu_category</code></li>
<li>Drag-and-drop ordering on the admin list screen (uses <code>menu_order</code>)</li>
<li>Shortcode <code>[wrmj_menu]</code> with category filters, order, limit, and grouping</li>
<li>Settings screen to adjust defaults and display options</li>
</ul>
Text Domain: <code>oishii-menu-board</code> 
Domain Path: <code>/languages</code>

Oishii Menu Board

Manage single-item restaurant menus and display them via shortcode. Supports drag-and-drop ordering for categories and items.

Risto Niinemets

Most commonly taxonomy sorting plugins will create a new interface to drag or order/sort your terms. This plugin uses the built-in view just to make things easier. Just grab the term and drag it to a new position. No more extra clicks – everything is saved after repositioning!

The Taxonomy Sort

I would advise against using this plugin. In the latest WordPress update, selected categories are no longer displayed on the posts page. Deactivating the plugin shows the selected categories once again. It's too bad, this was a useful tool.

Broken in WordPress 4.7

Allows you to easily change the order of different taxonomies/terms/categories.

Oishii Menu Board vs The Taxonomy Sort