The universe is of infinite dimensions. It is ever-expanding. If we assume the surface of the universe is 2D (Like the Earth), then if you walk far enough in the same direction you will get back to where you started from!
Of course, the space between distant galaxies is expanding so fast that you'd be hard pressed to make any real progress outside of our cluster of galaxies.
Take this analogy: Small stickers glued onto a balloon, the balloon is inflated. If you are on a sticker, the space is not expanding under your feet. If you venture out of the sticker (out of the tightly grouped cluster of galaxies) then it will be expanding around you. Depending on the rate of inflation of the balloon, you may not get anywhere! (It is even possible that as soon as you step off the disc any space between you and the disc will begin to expand rapidly - so you may never be able to get back to the disc! But in any case, traveling to the edge of the galaxy cluster is about as impossible as anything else at this point in time... we can't even travel to the edge of out Solar System let alone galaxy!)
If you say that the universe is more like a balloon with the galaxies floating around inside and the balloon is expanding, then in theory you could check out the edges of the universe, and then use that information to predict where the centre of it was! Of course this too would be highly impossible at this point in time! In theory the universe could go on to infinity... with more sparse distribution the further out you venture. Like prime numbers, first theres lots of them, and as you get to larger numbers primes are more and more sparse! At one point the next prime will be too far away to be visible, but that doesn't mean it is the last prime, and you have reached the edge of the prime numbers...does it? So how do we really know if what we see is the end of the universe, or just a really big gap between this galaxy cluster and the next...
I don't think I know enough mathematics to know if it is possible to predict the origin of all these galaxies without a reference point. It might be possible to use the direction of motion of other galaxies to triangulate in to the origin of motion... the location of the Big Bang, but that too is quite impossible seeing as we can't even get an accurate prediction for the Hubble Constant. Let alone accurately measure not only the speed, but also the direction of these receding galaxies.
If you assume that the universe is 4D, then it could in fact be in a twisted Klein Bottle configuration. So if you did attempt to reach the edge you would never find it, since there is really only one side! This would mean though, that the universe is 2D. It going along the surface of the klein bottle, which of course has no edge, much like a sphere.
With all this said, I am confident in saying that I am at the centre of the universe. The universe revolves around me (for the sake of cliche). Everything else is moving away from me. The big bang was right here. Now prove me wrong and I'll stand down.