You can get much better than two orders of magnitude savings off of conventional rocketry alone. Also note that fuel cost is one of the least important costs of rockets, even though the rocket equation requires you to carry that basically meaningless cost stuff up with you. What makes rocket fuel expensive, in orbit, is the cost of getting it there in the first place.
For example, with a Space Shuttle launch, the catering budget for the press corps covering the launch was more than the cost of the fuel used for the launch, at least for the liquid fuels being used. Far more was spent simply on the general labor that was used to essentially rebuild the Space Shuttle after each launch... especially the SSMEs.
I'll admit that perhaps some other alternative approaches to spaceflight including the classic Orion nuclear fission launch system might end up being cheaper and more efficient (definitely NERVA), but you need to consider infrastructure costs and regular maintenance as well when considering these other alternatives for getting into space.
Space Elevators in particular must be made with a mythical substances that as of right now simply does not exist. This Unobtainium must exhibit properties that no known substance has ever been demonstrated to hold at astronomical scales of construction that have never been attempted in the entire history of humanity. I also think that infrastructure costs for a space elevator are likely to be far more than proponents claim they will be, and more importantly a space elevator is completely incompatible with any other launch system. I think it is that last point which completely destroys at least a terrestrial-based space elevator.
A space elevator on the Moon is much easier to construct and can be done with high tensile strength materials that currently exist, and it wouldn't conflict with most other transportation systems including rail guns and most classical orbital inclinations that could avoid at least a few space elevators on the Moon. Some larger asteroids might especially be excellent candidates for space elevators, so I don't think the concept is completely devoid of consideration.
I am merely suggesting that an Earth-based space elevator is a hopeless dream until we have several hundred years of additional technological development in material sciences alone.