I like site icons. Some folks don’t think they’re necessary, and technically they aren’t. But it sure it nice to see one in your browser tab and in your Bookmarks Toolbar, if your browser is so equipped and you’re putting it to good use.
I like that teeny, tiny bit of color that helps distinguish one site from another at a glance. I make full use of the Bookmarks Toolbar. I have icons across the full width of my screen. I had this when I was using Chrome and now also in Firefox. This is one of the reasons that, even though I work on a Mac, I don’t like Safari. It takes all the color out of the icons and makes them shades of gray. (I’m not sure if there are 50.)
How To Add a Site Icon to Your Site

I obviously haven’t checked every theme, but I think it might be a standard feature of WordPress now to have a way to add a site icon under the Customize menu.
Here in Astra, I had to hunt for it a little. I eventually found it under Customize > Layout > Header > Site Identity (scroll to the bottom of the Customize sidebar).
It used to be that you had to make a graphic a certain size and upload it using FTP to the files area of your site. For a while, it was supposed to be really small. Then there was a time when it had to be quite large. These days it doesn’t seem to matter what size it is.
You also had to name that uploaded file with the .ico file extension. Today, as long as it’s a jpg or a png file, you’re good to go.
Where Can I Get a Picture to Use As a Site Icon?
The simplest way I know of to find a decent site icon, is to do a Google Image search. A site icon is so small that it doesn’t pay, in my opinion, to spend a lot of time or money on getting one.
In the Image area of Google, be sure to click the Tools menu, then Usage Rights, and then (for most sites) Labeled for reuse. This will get you free graphics that you don’t have to worry about paying fees for or infringing on anyone’s copyright.
When looking for the icon for the WP Inn, I searched for inn clipart. This got me some clean, bright results. I picked one from Pixabay that, as you can see, shows an inn (house) with two windows and a yellow, thatched roof. It looks inn-esque enough for me.
What do you think?

