You're going to get the usual objections that we can't answer except in the limit as one goes faster and faster; obviously for massive entities like us actually attaining the speed of light is off-limits.
As one gets moving faster and faster (relative to some space-permeating lattice of clocks which are equidistant to each other and in sync in their coordinate system, say), many things happen:
- Everything that they can see "crowds into" the point right in front of them, except for the single point immediately behind them.
- The lattice also appears to be length-contracted; at higher rapidities $\alpha$ the speed these things are coming towards you is approximately a constant $c \tanh \alpha \approx c$ but the distance between them goes to zero like $\ell / \cosh \alpha.$ Therefore you appear to be passing more and more and more of them per second of your time.
- These two effects of the stars wanting to tilt "forward" and the things you're passing flying backwards past you seem to meet up at a definite distance behind you: your uniform acceleration effectively creates an event horizon at a fixed distance behind you; things which pass you appear to fall towards this and redshift into stasis rather than fully disappear. However this wall of death is actually an effect of your acceleration and if you were to stop accelerating it would fall back further and further behind you, as the tilt "forward" stopped increasing.
- Clocks which appear on the lattice appear to be getting time-dilated more and more, going slower and slower.
There is, technically speaking, no "limit where one accelerates all the way to the speed of light." The problem is that everyone measures light travel at the speed $c$ in their own local coordinates, so no matter how fast you start going, you still have an infinite distance to go! I like to refer to this as a "real-life Zeno paradox".
But we can try to stretch our imagination, to try to figure out what would be happening if you took these trends as far as they may go: for example, all of the stars crowding into the one point of the sky suggests a one-dimensional existence, but all of the inter-object distances shrinking also suggests that this line is only a handful of real honest-to-goodness points. So one might imagine that one needs to think of a sort of zero-dimensional three-point existence, there is the point where the photon "is" between emission and absorption, the entire future-pointing light cone of events appears as one point in front of it, and the emission event and its past-pointing light cone of events appears as one point behind it. There is no "time" per se as the photon hops from the first of these points to the middle to the end point; there are just the two transitions where it winks into existence and winks out, and as far as the photon is concerned they just happen one after the other.