I excluded any other source of light for the sake of simplicity, so imagine you racing against light from a laser. If you were faster, then you'd arrive at a pitch black place.
You could also travel faster than the sun's light wave, but then when you reach the "pitch black area", it would be 5(?) billion light years away. If the sun was 4 billion years old, you would be 4 billion light years away. (Im not sure how old our Sun is).