The balloon analogy while flawed is nevertheless quite a nice one. The point there is that you have to imagine the surface of the balloon as being the Universe. Then when you blow the balloon up and space expands, the "centre of expansion" is somewhere in the middle of the balloon -- and, crucially, not anywhere on the surface. Hence it is possible for the centre of expansion to be not a part of the thing that is expanding.
Where it falls down is that you can see the balloon as expanding into something. Unfortunately this is (probably) not what is actually happening. Instead, the Universe creates its own space as it expands. I suppose it would also imply the "hole" that you are thinking of. Again, the balloon analogy can help if fully understood -- people living on the surface of the balloon can only perceive what is going on on the surface of the balloon and cannot see what is not directly on or part of the surface. Hence they would never be aware of the void in the middle (although a clever balloon physicist might be able to imagine its existence).
I say probably, because firstly in a "multiverse" picture it sort of follows that there has to be a meta-universe in which all the various Universes are sitting; and even without other Universes there is nothing to stop you just inventing a further dimension that extends beyond the confines of the Universe in which we live and can provide a real sort of "space" beyond it. These are very tricky concepts although the mathematics is not too difficult once you get your head around the notation. The key concept to read up on is that of a manifold (google it).
As Old geezer has said already, there is no "centre" of expansion, then, in the sense of a point in space you could visit and say "here is where it began". Because the entire universe was created at the Big Bang, everywhere you stand was once at the very same point and so you are at the centre of the universe. And so am I. And then neither of us are, in a sense, as well, as the "real" centre isn't a part of the Universe, just as for the expanding balloon.
Thanks PP for singing my praises although it should be stressed that while I am a professional physicist, I spend most of my time working on the physics of tiny particles and don't normally get that involved in Cosmology, which is at entirely the other end of the scale of physics. Still, hopefully my experience elsewhere counts for something.