Al said "Smack in the middle of the dark side."

The cable has to rotate with the surface of the planet. The dark side will be light side in 14 days.

gbaikie said "For a space elevator you need to get to Geostationary orbit; on the Moon "Geostationary orbit" is Earth/Moon L-1 & 2 (or L4/5 which even further away)."

Wrong. The syncronous orbit surrounds the body it's orbiting. The lagrange points on the moon are fixed to the relative position of the Earth. This means they "move" with respect to any point on the moon's surface which
is no good for a space elevator.

gbaikie said "Now, with a Earth Elevator you also need an anchor- roughly, you get this by extending the elevator beyond GEO. Btw, I think the key to making a Earth elevator would be to have a massive object in GEO (a good size asteroid) and why this would be key is based on idea of the relatively cheap cost of getting a massive object to GEO and not needing to process on this mass."

This just isn't the case. Modern concepts of a space elevator (from Earth) involve extending the cable 3 times past
geosync so that the centrifugal and gravitational forces negate over the length of the cable. This way it's not under
high tension to the earth's surface and doesn't require anchoring to a mountain. This way if the cable is severed on the surface, it remains stationary and doesn't fly off tangentially.

You guys should look here at what those who do this for a living are doing.
http://www.isr.us/SEHome.asp