How to add div to top menu item

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When using wp_nav_menu you can pass arguments to it which help you style the output, look at:

  • $container Whether to wrap the ul, and what to wrap it with. Allowed
    tags are div and nav. Use false for no container e.g. container =>
    false .
  • $container_class the class that is applied to the container.
  • $container_id The ID that is applied to the container.
  • $menu_class CSS class to use for the containing div element which
    forms the default menu, or the ul element when a custom menu is
    configured in the admin interface.
  • $before Output text before the of the link.
  • $after Output text after the of the link.
  • $link_before Output text before the link text.
  • $link_after Output text after the link text.
  • $items_wrap Whatever to wrap the items with an ul, and how to wrap
    them with.

So in you case you can use 

array( 'link_before' => '<div class="your_class">' , 'link_after' => '</div>');

But if you ask me you can probably do what you want with the classes WordPress prints out anyway.