Where to store JS and CSS that is not associated with a module?
My gut feeling would be to place it in a folder in the root of your website and access it through a subdomain. I'm not sure, without knowing more about the application, if there is an effective way to integrate it with Drupal. It seems like it should stand on its own, in it's own directory structure, as it is a separate entity. I stand to be corrected here, but i don't see a problem with hosting it concurrently with your Drupal installation. It won't be manageable through the CMS, but without building the functionality in Drupal itself, it wouldn't be anyway.