The whole universe is infinitely vast. It continues to expand so quickly that there would be no actual way of being able to catch up with it. This makes it incredibly hard to even comprehend what would be necessary to actually examine what it's like beyond our universe.
But say we had the technology to get us to the event horizon where the universe is expanding; then what? If this happened, by the time we got there, the universe would have expanded even further. Even at the speed of light, which still takes time to get from point A to point B, we wouldn't be able to catch up with the universe's expansion.
If the universe's expansion were to freeze during the travel, this might be the only way to get to the end of the universe, but even then, it would take eons to get to the universe's edge.
There are a lot of theories out there about what it's like beyond the event horizon, but there is no concrete evidence that anything else exists out there. There are ideas floating around that there are other universes out there, while others believe that we're the only universe out there that continues to expand at an exponentially growing rate.