Asking what is outside the universe seems like a sensible question however it obscures what the current model of the universe proposes. The universe is indeed expanding however there is no center that it is expanding away from. Every point can be considered to be at the center since from every point the rest of the universe is receding. So there is no edge and therefore nothing on the other side of the edge. The edge of the universe is like the edge of the earth. You can see the horizon but as you approach it, it seems to move away. This is because the earth is a 3D sphere. In a similar way the current model of the universe treats it as a 4D sphere. In theory if you went far enough you'd end up where you started. But due to the expansion of space you can never get that far before that recedes. In many ways the universe behaves like a black hole. Nothing, not even light rays, can get out because they are never near an edge (there aren't any edges). Thus if you could try to imagine being on the outside you would not be able to see the universe because the light in the universe couldn't reach your eyes. Current theories predict a multiverse, which is a higher dimensional space in which universes are constantly created like bubbles, but these would behave like independent entities, since influences (like light) cannot escape. Other versions of this theory predict that gravity is an interaction of neighboring universes (brane theory). These are of course speculative and no method to test these ideas have been developed.
