Where is the Void?

Question

Where is the Void located in the Ardean(?) universe?

After thinking about it for a while, I see three different possibilities:

1. Iluvatar's space [Arda (Void)]: The Void belongs to Arda, which are both located in Iluvatar's space.
2. {Iluvatar's space [Arda] (Void)}: Arda and the Void are parallel spaces in Iluvatar's one.
3. {Iluvatar's space [Arda]} (Void): The Void is outside of Iluvatar's space.

If Iluvatar's space isn't the name Tolkien chose:

It describes the space Iluvatar and all the Ainur who didn't go to Arda are staying.

Answer 1

Tolkien drew a helpful map to help with his cosmology. As you can see, Arda (the Earth) is set among the Void (Kúma), which is itself split into two parts; Kúma and Ava-Kuma (the Outer Void).

This ties in nicely with his description in the Silmarillion

arid they saw a new World made visible before them, and it was globed amid the Void, and it was sustained therein, but was not of it.

and

Therefore Ilúvatar gave to their vision Being, and set it amid the Void, and the Secret Fire was sent to burn at the heart of the World; and it was called Eä.

Answer 2

The Void is "the state of Not-being, outside Creation", and "outside Time and Space".

In a late 1950s essay titled "Notes on the Motives in the Silmarillion", Tolkien discusses the concept of Morgoth being thrust into the void, and talks a bit about it what that would mean, and whether Morgoth was actually thrust there or if he just merely left the Arda. Tolkien defines the void as "outside Time and Space, outside Ëa altogether", and "a conception of the state of Not-being, outside Creation or Ea".

We read that he was then thrust out into the Void. That should mean that he was put outside Time and Space, outside Ëa altogether; but if that were so this would imply a direct intervention of Eru (with or without supplication of the Valar). It may however refer inaccurately* to the extrusion or flight of his spirit from Arda.

* [footnote to the text] Since the minds of Men (and even of the Elves) were inclined to confuse the 'Void', as a conception of the state of Not-being, outside Creation or Ea, with the conception of vast spaces within Ëa, especially those conceived to lie all about the enisled 'Kingdom of Arda' (which we should probably call the Solar System).
_{Morgoth's Ring - "Myths Transformed"}