Comparative Military Bases
This series of maps is worth a look: What we can learn by looking at where world powers have military bases.
Here are two of them, the US and China:
While such maps do not tell all one might need to know they do undercut two arguments often made in the popular press.
First, it is hard to look at the US map and make the argument that the US has withdrawn from the world (or even has a new, smaller footprint).
Second, while China is a rising power and is asserting itself in its own neighborhood, its power projection capability is limited. Along those lines, it is worth pointing out that despite the small size of some of the red in Asia, there are a lot of US bases in Japan and Korea.
One note: I am unaware of a US military base in Brazil