I wish I could just check a checkbox and make certain Google Analytics data public.
I get that analytics can be a very private thing for some sites. I think there are just as many sites where that data just doesn't need to be private. Not only would it be interesting, but insight might be gleaned from having more eyeballs on the data, and it could contribute to a wider data set of analytic trends.
Anyway, there is no such checkbox. But Zach Aten pointed out to me there is a thing called Data Studio that allows you to build custom visual reports, and you can make them public with the same kind of sharing controls you find in other Google products (like Google Docs).
I slapped together a quick dashboard for just raw traffic data. Not the most useful thing to look at, but sometimes the most fun. I'd embed it here, but...
Can I embed charts on other sites?
No. Data Studio is currently a stand alone product.
Embedding a Data Studio report in an iframe is blocked by Chrome as a potential security risk.
Of course, you can do a way better job of not only building more beautiful and useful charts but also of collecting more useful data. If you're using Google Analytics, doing a little bit more than using the default snippet goes a long way. Remember we have an article and video on that subject.