Or go right. Time dilation would start working in your favor. You might get there, and back, within your lifetime. Of course everyone on earth would be long dead.
Micrometeors and radiation would be the major problem. Also, it's not just time dilation that would help. At relativistic speeds, space contracts quite noticeably in the direction of travel, so the actual distance you need to cover diminishes as well.
That's because you won't be locally faster than light. You may cover 4 light years in one, but only because those light years will be much smaller from your point of view. You'll never "feel" faster than light.
I think you may have misinterpreted what I said. I didn't claim that you'd feel like you were covering the distance faster than light. I was saying that as you go faster (relative to your destination), space contracts ahead of you so the distance becomes shorter than it would if you were moving slower.