Where do I put my favicon with Hugo

Put the favicon inside of the static directory. The static directory sits in the root of your hugo site. When you generate your site, the favicon will be copied into public, the root of the generated site.

Putting your favicons in static folder is right. It will be published to public folder once the page is built.

However, using absolute CDN (e.g.: Dropbox) services could be better for page performance.