|LEO Station||300 km||273 tons||0.999 g|
|GEO Station||35786 km||30 tons||0.38 g|
Of course, this is a much longer tether than in the film.. but hey, Danny Baldwin is in it - he doesn't make good movies. Anyway, the high station could be an ISS-style module with airlock and docking ports for satellite servicing vehicles. The low station would be a true permanently inhabited facility where people can live for years at a time without fear of bone mass deterioration or the other negative effects of zero gravity. To maximize space we may be tempted to use inflatable Bigelow modules, but we have to consider how they will behave in full gravity.
The only sticking point left is radiation. On the LEO station crews have much less exposure to cosmic radiation thanks to the Earth's magnetic field, however they receive just as much from flying through the South Atlantic Anomaly. As a result, radiation on the GEO station would be 2.19 times as high during solar maximum and 6.568 times as high during solar minimum. If that seems confusing, just remember that the Sun's magnetic field provides most of our protection against cosmic radiation, and it does that more at maximum than at minimum.
One solution may be minimagnetospheres but, again, technology developed for zero-g rarely works unmodified in full gravity. The best solution may simply be appropriate mass. The requirement that the low station be 9.1 times more massive than the high station means that both will have to grow simultaneously but getting mass from LEO to GEO is pretty easy when you have a tether joining the two altitudes.
You may be asking: how plausible is this? Or even: isn't this just the Space Elevator? I estimate it is at least two orders of magnitude easier to do than a space elevator and would only require (vast amounts of) existing tether materials. The cost is most likely dominated by launch costs that should be around $800M in a few years time.