We may be able to travel a few tens of percent of the speed of light or a few hundred MILLION miles per hour. This would make travel within the solar system a hair-raising experience, but the nearest stars would still be decades away. To get the full benefit of relativity, you need to get to 70 - 80 percent the speed of light or better to get time dilation factors better than a factor of two. Because your inertial mass grows with velocity, more power is needed to accelerate to the higher speeds, and the net effect is that a spacecraft of human dimensions and mass would require the annihilation of something like its own rest mass to make the journey possible. We don't know how to do that in any controlled way, and I suspect that truly relativistic travel will be economically impossible. Still, there is a lot to see in our own solar system, and we might be able to send micro-gram sized spacecraft to other solar systems. Upon arriving, they would have to manufacture a radio telescope a hundred meters across to beam a signal back to us. It is not obvious how to make such a machine....yet.