If you were to travel to the nearest star with speed 0.99c (99% of speed of light), you would not experience the travel to take 4 years, your perception of the time would be shorter because of the time dilation effect of special relativity. Once you'd come back to Earth, you would find out that at least 8 years have passed, though. By moving at a speed close enough to the speed of light, you could
travel any distance in your lifetime. This effect explains why
high-energy muons formed in the upper atmosphere can reach the earth's surface even though muon's t
1/2 is so short that they should decay on their way down.
A good mental image of this is that because time and space coordinates are treated equally in relativity, you can not only use kinetic energy to travel faster through space, you can also use it to travel faster forward in time without aging in the process yourself.
The idea of bending the spacetime around a spaceship to be able to travel faster than light is the subject of NASA scientist Harold White's research:
https://en.wikipedia.org/wiki/Harold_G._White
Making that "warp drive" would require exotic matter with negative mass energy density, though, which is highly speculative.