The nearest neighbor to our over own Sun is Alpha Centauri. This star is at a distance of 4.37 light-years from sun which is nearly 41.343 x 1015 m.
Lets be optimistic and suppose we find out a way to travel at the 100th part of speed of light (which is close to impossible), but suppose we found. Now assuming that we travel at this high speed, the time we take to reach Alpha Centauri is
If you see the magnitude of 100th part of light, it is 10792528.488 km/hr, and that is HUGE. Attaining such high speed is, till now, practically impossible. Hence at least in this lifetime you cannot get anyway near Alpha Centauri.
We now have no clue about what technology will exist 1000 years from now, but we all would love to go on a space trip and visit our closest star after sun.