well, starting on the moon could be an idea, assuming that the materials nesesary for the construction would be redily available. But at that point, one would need a moon "base" of operations. And getting that to the moon in the first place could be an issue. after the space elevator is completed, perhaps a second facility could be set up to build and mass produce the CNT, etc, or materials required.
But... this may be a suggestion for the ribbon... Has anyone ever tried to "construct" or assemble a cnt in zero gravity??? orbit.... would this even be possible given the equipment required... would the flaws become more numerous, or would they become scarce...

Something to look into for when the first elevator is fully functional.
dan