Consider a space elevator, a thread hanging from the heavens and being anchored to a spot in ground or sea barge at equator. As I understand it, it'd be very thin at ground and get thicker on the way up to GEO, and thinner again towards the counterweight station at the end. Construction material is basic pure carbon nanotube in this case.
Added details: I'm thinking of an early space elevator, with payload capacity in single digit metric tons. Hmm, how it is powered might radically affect how the whole thing looks like, but to avoid altering the question, it's ok to assume it does not.
What does it look like? What color is it? Would it glisten in sunlight, upper parts looking like a spear of light at early/late nighttime? Or would it be coal black, visible against blue sky as a black thread? Or something else?
Would the elevator need coating, paint, against UV light or water or anything else? Could it even be painted? I think not, weight would be too much. But if yes, perhaps atom- or molecule-thick layer of something that would stick, how would this change coloring options?
Edit: I'd prefer as hard-science answer as possible. For those suggesting paint and even lights, weight of the paint (this fortunately scales r²) vs. weight of the payload (this might scale r³, unless there are some factors I'm not aware of) would be important. Something to think of about this: the cable has carry the weight of the paint plus the extra weight of the cable below it needed because of the paint.