You need a comma after the state or year as in the following.
Joe was born in Hollywood, California, on January 14th, 1919, right after World War I.
We don't catch this because most of the time we end the sentence like this:
Joe was born in Hollywood, California.
Or we have a coordinating conjunction (FANBOYS) between two sentences like this:
Joe was born in Hollywood, California, and he was born right after World War I.
So we usually miss it when we start creating more dynamic sentences like the first example above.
Now look at this:
Joe, who was born in Hollywood, was born right after World War I.
If you're having problems remembering this comma rule, then think of it as expanding the idea of the location or time, just like in the above sentence where we repeat the idea of who Joe is, and therefore need to surround it by commas.