Widgetizing Header

I want to widgetize my header to show a dropdown list of particular categories/pages. The dropdown widget have to be located between the site logo and the social links. Any guidance or thoughts on achieving this?

It might be more difficult than it might seem.

First of all you need to register new widget like in this given example

// Registering header widgets
register_sidebar( array(
	'name' 				=> __( 'Header', 'travelify' ),
	'id' 					=> 'travelify_header_widget',
	'description'   	=> __( 'Shows widgets at header.', 'travelify' ),
	'before_widget' 	=> '<aside id="%1$s" class="widget %2$s">',
	'after_widget'  	=> '</aside>',
	'before_title'  	=> '<h3 class="widget-title">',
	'after_title'   	=> '</h3>'
	) 
);	

You can tweak this if you need different classes, heading tags etc.

Now you should add this code where you want your widget to appear in the header. Most likely you want it to add it inside header-extensions.php file which is located in theme folder - library - structure.

<?php
	// Calling the header widget if it exists.
	if ( !function_exists( 'dynamic_sidebar' ) || !dynamic_sidebar( 'travelify_header_widget' ) ):
	endif;
?>

Furthermore you will have to style this widget and probably change styling for right and left header parts to make new widget area to fit between them.