Q: Why isn't the space elevator atop a mountain, like Clarke's was?
A: Clarke posited that the shorter the trip into space, the cheaper the elevator would be to build. Also, the trip up (and down) would be shorter, the mechanics of the thing more reliable, and all that.
The one thing Clarke did not consider was the logistics of getting people and materials on and off the elevator. That’s why Hammer built his elevator near Chicago, in the center of the U.S. and near railroads, highways, and air transportation. Hammer saw a burgeoning space-based industry on the horizon, and located his elevator accordingly. By contrast, to get to Clarke’s elevator one must first travel into one of the less-accessible parts of the world.