@blueveinedthrobber,
The universe is thought to be finite but unbounded.
A good analogy for this is to look at the surface of a balloon. In the 2-dimensional surface of the balloon, there is no edge. If you use a marker to draw dots on the balloon, and blow the balloon up to a larger diameter, the dots get farther apart, but there is no "center" within that 2D surface. Each of those dots could represent a galaxy (or even a galactic cluster). By the same token, the universe is expanding, but there is no center in the usual sense.
The 3D space of the physical universe is similarly finite but unbounded, with the "radius" being in the 4th dimension (time). Like someone else said, if you go far enough in one direction, you end up where you started. Only you'd have to travel far faster than light to appreciate that. At the speed of light you'd return to a Milky Way galaxy that no longer had Earth and the sun. They would've died billions of years earlier, and all that would be left is a feeble white dwarf and perhaps four planets. All the familiar constellations would have disappeared near the beginning of your journey.