LEO ain't far away. If we ever get a space elevator, I could imagine people working on asteroid placed in LEO following the same kind of schedule people on oil rigs follow now.
Earth to LEO via a space-elevator? Unless you have a good way to step sideways (and thrust sideways) 4/7ths of the way up to the GEO station, that sounds like a hassle. Unless you
need to be in LEO (manual geosurveying with a Mk1 Eyeball? ...or ongoing manned operation/maintenance of some other downwards-pointing station that works better 'that low down'), I'd say move everything 'commutable' up to GEO, either on the tether itself of forward/backwards in the orbit[1]. Everything that doesn't have some other requirement (most of which will look to be in a higher-than-GEO station, or something elliptical/polar/whatever).
(I'd also like it if the mechanism to detach the cable-car from the cable was there only for emergencies, and not a routine thing to do, with a short dizzying time of disconnection before the required boost was initiated to attain the 15,000kph or more sideways (eventually) orbital velocity. OTOH, I'd quite like the capsule to
have disconnect and re-entry capabilities. Still I don't see space-commutes ("No, I live in Iowa, I only
work in space") this side of a Matter Transporter system, or something involving inertia-immune/proof hi-performance transfer vehicles.)
[1] Perhaps Eventually get yourself a ring of stations (whether you connect them up, or not). But how much space do we need in space? Although attaching line-tops[2]
[2] Well, not quite tops. The actual tether 'tops' would have the inverted counterweight station with the 'bomb bay'-styled free energy probe-launching system in it, for easy interplanetary launches.