Answer

This question takes us back to the question of tzimtzum, divine contraction. Precisely because of your argument, some have claimed that God did not contract Himself and is still present everywhere. Moreover, we and the world do not really exist, because if we are not Him, then that would limit Him, since there would be something outside of Him. They claim that the contraction is an illusion, our perception rather than actual reality, but that is of course nonsense. An illusion of whom? In reality, if we are Him Himself, then who exactly is being deluded here? In whose consciousness does this illusion take place?
Therefore it is clear that there are things outside the Holy One, blessed be He: us and the other objects in the world.
Now you can ask whether this is not a refutation of His being unlimited. To that one can answer in several ways: 1. No, because He chose to contract Himself, and by His will He can return the world to tohu va-vohu, primordial chaos, so that only He exists. That is not a real limitation. 2. The contraction took place in a lower dimension. We live in a world of three dimensions, and one can view the Holy One, blessed be He, as existing in a higher dimension (4, or if you like, infinity. Of course I am not speaking only about spatial dimensions but about any parameter you wish). In such a situation, three-dimensional objects do not subtract any part of the space of the higher dimension, just as an area subtracts nothing from the volume within which it is contained. See Mishneh Torah, chapter 17 of the laws of the Sabbath, regarding a side-post made from asherah wood. Therefore there is no limitation on Him here.
There is a series of recorded lectures of mine on the site about tzimtzum, and you can see a fuller explanation there, although if I remember correctly the series was more than three lectures:
 https://drive.google.com/drive/folders/0BwJAdMjYRm7IRmkxVjZRdmRmWm8