Hello
I asked quite the same question as it seems strange not to have a good tool to do that.
You will find a nice discussion on this subject.
I see that my tool in Nautilus plugin has some limitations, no more than 100 hexagons on a row. I could easily change that if my tool is interesting for your problem.
I just made the change in my own tool (could send it if necessary) and it works
And if you want some centers just use Polygon Center it will outputs 2 types of center and not area center as polygon is not flat.