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The big problem is energy. If we had almost infinite energy we could accelerate to a significant fraction of the speed of light at a leasurely 9.81 m/s² in about a year. The travel at almost lightspeed would feel instantaneous for us. Add another year to decelerate at the same rate. We could reach any point in the visible universe in 2 years.
Our destination would just be drastically different from what we observed, depending on how far away it was.
Oh, and apart from the tiny energy problem cosmic radiation will probably destroy our spaceship. I bet at relativistic speeds you'd even get enough neutrino collisions to make them a problem.