Gravity repellent material will be far away.
Without attempting to math it out, the presence of two materials, one attracted and one repelled by the dominant force at work on macro scales, will result in two separate halves of our universe expanding away from each other.
Lets call this gravity-repelling matter 'nega-matter'. Assume the universe was created in the big bang as a mass of hot expanding matter and nega-matter. Wherever there is a more dense lump of matter in the initial soup of creation, that point would at the same time attract more matter and repel more nega-matter than other points in the expanding universe. As more and more matter coalesced into the matter part, the power of repulsion would be greater and greater on the nega-matter.
You did not specify if the nega-matter has its own force that attracts it to itself, which is relevant for the final shape of your universe. If nega-matter is self-attracting, then it will also try to coalesce while being pushed away from regular matter. From a 3-d space perpective, there will eventually be a plane where one side is an expanding matter universe (like ours) and the other an expanding nega-matter universe.
If nega-matter is not self-attracting, then our universe will expand as it does today, with a spherical 'shell' of nega-matter being pushed outwards just behind the event horizon of the big bang.
In conclusion, either way there will be no nega-matter anywhere near us for us to observe. In the second case, the existence may be inferred from the cosmic background radiation somehow, in the first case, it seems unlikely that we would be able to recognize the nature of an expanding mirror nega-universe.