No one will get off at geosynch altitude. The point is to achieve escape velocity, which would require travelling out far enough to where you can just let go and will have the energy leave earth's gravity well immediately.
http://www.mit.edu/people/gassend/spaceelevator/center-of-mass/index.html
Ok, here's another page, that I found fascinating and enlightening, and it proved my intuition correct! CG slightly beyond geo.
But if you don't get off at geo, then you need to be really sure that the cable won't snap while you are on it. Because beyond that point, if anything goes wrong with the elevator, then you are in serious trouble. At least don't put a space station at the anchor.