Sorry for the radio silence on this topic, this is the first chance I’ve had to look at it since I was invited to comment a few weeks back.
A space elevator is definitely possible. There are many technical challenges, but the basic concept is feasible, as shown in several studies (I believe the studies, regardless of comments to the contrary on this community.)
I’m not sure if it is really workable, though. From legal issues to space debris to lightning strikes, there are things that would get in the way. The initial cost might be insurmountable.
However, I think that it could work very well on the moon, if a human habitat were placed near the equator. If humans end up near the poles, well, there are other sci-fi ideas for linear accelerators, etc.
ErnieRogers’ idea is a workable one that I have seen before that could work in orbit around Earth. Again, some technical challenges remain, but his concept is probably “easier” than a true elevator.
A challenge could be useful for this, if it were designed well. NASA did a challenge on elevators, though, with helicopters holding tethers and robotic climbers climbing the tethers. I’d start there, look at some of the papers and books that exist (I can’t spot the one on my shelf right now, but the NIAC Study at [http://www.niac.usra.edu/files/studies/final_report/521Edwards.pdf] is a good place to start) and find some of the long tent pole technologies and design a study around one of those.