The Media Uploader in WordPress 3.5 introduced major improvements, but it also removed the upload path option from Settings for simplicity and to prevent errors. This change streamlines the interface to a single checkbox for year/month folder organization. As experienced WordPress developers, we've relied on this customization for client sites—here's how to safely adjust the default media upload location.
Important Note: This guide is for advanced users only. Incorrect changes can break your site—back up wp-config.php first.
To modify the upload directory, edit wp-config.php in your WordPress root. For a custom folder like wp-content/files, add:
define( 'UPLOADS', 'wp-content/files' );
For an external directory, such as https://www.example.com/files/, use a relative or absolute path:
define( 'UPLOADS', '../files' );
You can still enable year/month folders via Settings » Media.

We've used these techniques successfully across numerous WordPress installations. Questions? Drop a comment below—we're here to help.
Function Reference / wp_upload_dir - WordPress Codex
WordPress Trac #21720