The newest version of any Tableau product is always available on Tableau's website. For Tableau Public specifically, the newest version can be found in the following link:
For more information on Tableau upgrades, I highly recommend giving the following article a once-over. Compatibility between Desktop and Server isn't really something to worry about if you're only using Public, since Tableau Public will always be on the latest version, but in other cases this article is extremely helpful:
Hope that helps!