Create site columns based off the taxonomy you want to expose, then set a default value with the term you want. Then make sure all content in the site consumes those columns.
Also create a unique content type for your home page, and make sure your custom columns get added to that. This makes it really easy to write a search query that says (for example), "Give me all the sites whose department is Finance"
If you have a site provisioning mechanism you can hook it into that. If you're creating sites manually, you'll need to either do this manually or execute a script to do this.
It is, in fact, possible to use web properties to tag sites. Do a web search for "indexed web properties" and you should be able to find how to do this. But I think the site column approach is more useful. It all depends on how you want to consume the tagging.