Migrating Multisite Setup to Localhost Running Nginx 404 for /files
I sorted this out. I'm using VVV Varying Vagrant Vagrants for my local development environment, https://github.com/Varying-Vagrant-Vagrants/VVV 

Needed to customize the nginx configuration files for my site to accommodate a Drupal installation. The issue with the /files folder contents being 404 was largely due to this. After I configured nginx correctly for Drupal it worked like a charm.

You can find a sample config file here for Drupal: https://www.nginx.com/resources/wiki/start/topics/recipes/drupal/