I think what you're looking for is 'behaviour flow'.
We use this little feature on our site to see where visitors are landing and then see how they're progressing through the site and ultimately seeing where they drop off.
As per Google, "The Behavior Flow report visualizes the path visitors traveled from one Page or Event to the next."
When logged in and viewing your site data, simply click on 'Behaviour' from the left hand menu, and then select 'Behaviour Flow'.
From there you'll be able to customise the way you see data and visitor flow - you can set your start point at a particular page, a city or country, or any Google Ads.
Google: About the Behavior Flow report
Google search for "google analytics Behaviour Flow" offering a wealth of advice and other webistes
It really is a great little tool and is good for picking up patterns and trends on high traffic sites.
In the interest of fairness for other platforms, Piwik also has this feature, called 'Transitions'. You can read about it on their features page, here.
I've been using Piwik on personal sites for a number of years now - it's a great tool!