You need a pretty good POD for German colonies in the Americas. With a 16th century POD there are basicly two problems. First of all the emperor was a Habsburg, just like the rulers of Spain (and for quite a while the same person, Charles V) and Spain basicly claimed all of the Americas (besides Portuguese brasil) for itself. A treaty made by the pope. Sure the English, Dutch and French simply ignored it, but I doubt the Habsburgs would themselves would. Secondly, there basicly was no Germany. The Holy Roman Empire was divided into several more or less sovereign entities and they would not care about some colonistation dreamed up by the Emperor (or whoever).
So you need a relatively early POD in the 14th or even 13th century, before the discovery of the Americas by Columbus. And in that case it doesn't matter. All of America would be a good place for a German colony.
Or you need a later POD, for example a different 30 year war with a better conclusion for the Emperor leading to a more unified Germany (or even a divided HRE, with a significant part independent of the HRE, but the rest closer to it than OTL). In that case you are almost too late for German colonisation (especialy considering that afterwards Germany needs to rebuild before they can start colonising), since Spain, England, Portugal and France already have significant claims and presence in the Americas. It ould be hard for Germany to join them on an equal level. Sure they might get some islands or small parts of the mainland (like Denmark, or Sweden or even the Netherlands had OTL), but the prime territory is lost to them.
Maybe, and this is a big maybe, they could start colonising the western coast of North America, but I think that would only be possible in the late 18th century and Germany would need some kind of presense in Eastern Asia to do that.