In the currently dominant theories, the Universe is basically the same everywhere, if you look on a large enough scale. There may not be a furthest star from Earth at all (the universe may be infinite) or it may be like "the furthest point on Earth from London" which exists, but is not a specially interesting place. The distinction between those two possibilities is exactly whether the universe "curves in on itself" (in which case it is finite) or doesn't in which case it is infinite. We don't know for sure, but any curvature is definitely pretty slight.
To see the universe as uniform, though, you do have to look on quite a large scale (billions of light years). On smaller scales than this the distribution of galaxy clusters (and so galaxies and so stars) is quite uneven, and there are places where there are no stars close enough to see with the naked eye. Nevertheless, with a big enough telescope in one of those places you would still see stars scattered in all directions.
You mention the big bang, and what you write suggests a common misconception -- that the Big Bang happened in the middle of a big empty space into which matter expands. That is not what the theory suggests. Instead all points in space, when you trace things back far enough, seem to have contained a very hot, very dense, sea of matter, which, as far back as we can extrapolate, was all spreading apart, creating new space uniformly spread throughout the old space in the process.