There are three theories for the shape and structure of the universe:
It is flat (Omega = 1): Local curvature and geometric curvature is flat, the universe is infinite in all directions, and always has been. If the universe is flat, that means there is no boundary, and A: you will travel forever and only see stars, or B: stars range has an end and beyond that is an infinite void.
It is Closed (Omega > 1): There is a positive curvature; travel in one distance far enough, and you will end up back where you started. The universe is a plenum. Asking where the boundary to the universe is if the universe was closed would be like asking what's beyond the Boundary of the Earth.
It is Open (Omega < 1): There is a negative curvature; the universe is expanding. It will expand until either gravity overcomes expansion and the universe collapses in a big crunch, or it will continue to expand forever, until matter ceases to exist in either the big rip, big freeze, or Heat death. In this case, the universe is expanding faster than the speed of light, therefore it is impossible to reach the boundary (It is postulated that the Universe is a baby universe inside a black hole.) If you could somehow go faster than light, you would find nothingness. Not even an infinite void, it would not be logically possible to describe this area.
Current calculations seem to indicate that the universe is Open, that it is expanding (not just expanding, but accelerating!) and that the universe will expand and will eventually experience a heat death.