I mean the universe is so incredibly vast that even if we figure out how to travel at the speed of light, we'll only ever get to see a small fraction of it. I don't think we'll have to worry about running out of places to explore.
So we could definitely explore the universe, we just have no way to share what we discover with our friends back home.
True, but on the other hand, due to relativistic time dilation, a very fast traveller could visit very far away destinations if they get closer and closer to the speed of light.