You are getting relativity wrong. The layman phrase being used here 'time come to a halt and disappear' encodes what would happen from a relativity perspective. Everything that you would be seeing relative to you, would appear as if time had stopped if you were traveling at c.
If you were traveling at C you would not really see anything [external] at all. Length contraction would be such that everything around you would appear as a single motionless point.
Any incoming light would be blue shifted to infinity, or red shifted to zero, so if any actually touched you there would be infinite energy there. Luckily no light can actually reach you - nothing can. You would have no incoming sensory information at all.
Because of length contraction there's no distance between the start and and of your journey, so from your POV it doesn't take an time at all, since the distance was so short.
Not so fast :) Your own time would not "come to a halt and disappear", would it? If something travels with you at the same speed it would not get frozen in time. So, "everything that you would be seeing" is a bit too inclusive.
Here is what I've found to be the most intuitive way to think about it: everything is always moving at the speed of light through spacetime. When you move through space you are not changing the magnitude of your velocity (through spacetime) at all, only the direction. So the faster you move through space, the slower you move through time. If your velocity through space is v (relative to some reference) then your velocity through time is sqrt(1-(v/c)^2) seconds (from your point of view) per second (from the point of view of the reference against which you are measuring your velocity through space). When v=c, then you are moving through time at zero seconds (from your point of view) per second (from any point of view moving at <c). So your time never advances. You get where you are going (and everywhere in between) at the same time that you left (from your point of view).
