On that note, I don’t know if there’s any website that will have your browser request the root page on various sites and return one with a low average time – probably one out there somewhere.

Fediverse.observer does show the country that one is located in.

If you’re on a Linux system, there’s a utility which is designed to check ping time to a list of servers and find the one with the shortest average network latency called netselect. That isn’t necessarily the one that will serve up pages the quickest, since it could be that the server software is overloaded, and that it takes it longer to build the page.