Space elevator would be the most economic form of travel most likely, since in one comic it does reference humans having advanced development of structures in Earth orbit. (Don't remember the strip number).
It would be ECONOMIC but I doubt its FEASIBLE.
They have a material that theoretically could do it, yes. But that doesnt change the fact that any object hitting the elevator will have a massive impact. Practically it will be bullets flying at about 8 km/s, much stronger than normal bullets (which are between 300 m/s for subsonic bullets and something like 2 km/s for amor penetration bullets). And thats assuming we talk about satelite objects in fixed orbit. Meteors will have even greater speeds. I talk about the lower end of the elevator here, though. The upper parts will see much smaller impact speeds.
Besides, space elevator only means you have a fast way to get to geosynchronous orbit at 36,000 km from earth (at 36,000 km, you will orbit earth once every 24 hours, thus being always above the same point of earth. Thats why, by simply going up, you would be able to enter a stable orbit.
For example, it wont allow you to easily get to the international space station, which is in an orbit of ~350 km, which is cheap to reach (with normal rockets).
You still could try, though. If you leave the elevator at a point before the geosynchronous point, you would enter an orbit that would fall to earth in an eclipse. If you choose the right point, your lowest orbit point would indeed be 350 km. If you slow that orbit down, you will be able to enter the 350 km orbit at much less needed acceleration than directly starting with a rocket, and more importantly, as you dont need to fight earth gravitation, you might use an iron engine for this, which produces very little thrust, but is extremely fuel efficient. It also needs a lot of electricity, but thats what solar panels are for. However, the travel time would still be so slow its not really an option for manned flight.
The other option is of course leaving earth orbit altogether at points much above 36,000 km.