Will humans ever be able to travel the universe?

Even if someone built a spaceship that could travel the speed of light, it wouldn't even be fast enough to travel the universe. If you consider that Andromeda, the nearest galaxy to the Milky Way, is 250,000 light years away from our Sun, wouldn't that mean if someone was in a spaceship traveling to Andromeda at the speed of light that it would take them 250,000 years to get there? I doubt that they would still be alive when they got there.