The only way you could travel at the speed of light, not assuming highly theoretical faster than light (FTL) travel which actually bends spacetime to shorten the distance between two points (highly simplifying here), is if you transfer consciousness as information about it into a distant neural network or any other physical medium later supporting its function. So in that sense, you wouldn't see anything (or otherwise perceive information) about the environment that the information about your consciousness would have traveled through.
With FTL, and bending or warping of spacetime, it would be more like taking a shortcut. You'd see the shortcut at the (likely non-relativistic) speed you're traversing it as your point of origin behind you and destination point in front of you, but you wouldn't see the long way around path or anything from it, because you're not on it. If you can traverse this shortcut at relativistic speeds approaching some significant portion of the speed of light (c), then you'd also see objects behind you redshifting and objects in front of you blueshifting, and length-contracted space between two points at your sides.
If you're of mass though, be it baryonic or any other exotic matter that we have yet to directly detect, define, and work with, you simply can't travel at 1 c throught spacetime. Energy required for it is infinite, and you'd be of infinite mass to your environment, attracting spacetime towards you at the speed of light. You would have been, literally, the end of everything. You wouldn't see anything, even if you were some Marvel's superhero that can withstand the lack of reality, as time, from your vantage point, would have dilated to 1/∞. Form your point of view, the whole Universe would have collapsed onto you before you'd be able to realize you're in a bit of a pickle.