Well what I think is that the closer you get to C the narrower your point of view. By this I mean is an effect like going from a wide angle lens to a telephoto at full extension. One gives you a very wide view field and the other very narrow. At a significant percentage of C your complete view of the universe would be a narrow point of light straight ahead. But then that's what I have been able to garner from reading. I came across the very same question in a recent Dvice article.
Physics students at the University of Leicester decided to take on the task and do the math and this is what they came up with as you approach light speed and look out a view port:
Humm, not so far off! But exactly what are we looking at. Well in a nutshell the Doppler Effect. Matter of fact this shows that light DOES have properties that are wave like. But I digress as you travel, light waves ahead of you are compressed, this would "narrow" the field of view (and moves the frequency into the blue spectrum and then think about light behind you....and how we know the universe is expanding...hummm) of course as you get within a few thousands of a percentage the doppler would compress the light well past what the human eye can detect so there is a point where everything is completely dark.

