The 'getting off' point is geostationary orbit (22,000 miles ) so as to have a fixed anchor point you counter-balance it beyond 22,000 miles- typically a captured asteroid.
If you cut it at ground level, it would drift away. If you cut it higher, the cable would collapse to the ground, landing in a line west of the anchor point (you wouldn't want to be in the way - making Gabon or Equador a suitable site for this. Infact, the northern end of the Galapagos would be a brilliant site for it.
Yeah -a space elevator would be massively massively expensive - the most expensive civil engineering project of all time.
HOWEVER
It then makes access to space essentialy negligable cost. We could realistically begin programs such as the capture and mining of asteroids - potentially massive benefit to industry on Earth.
We launch about 50 rockets per year. That's getting on for something like 2.5 billion a year. Adjusted to modern cash, we've spent something like a hundred billion dollars getting into space over the history of the space program. Estimates range from $6 to $40B to build a space elevator - (or approx 1/3rd to 3 times the NASA annual budget ) - it would pay for itself quite quickly. We're not QUITE there financially or engineering science requirement wise yet....but nearly.
It is an elevator, and not joy-rides for rich people that will open up space to the general public. In the grand scheme of things - exceptionally cool though they are - vehicles like Space Ship Two will only ever be a gimmick.
Doug