Let me break it down for you:
1) Build space eleveator
2) Put spaceship docking area on the far end
3) Fuel spaceships
4) Send spaceships on their way without having to break the earths gravity, greatly increasing their efficiency and reducing the amount of fuel they need to carry.
Space elevators are certainly feasible by our current technology standards, we just need someone to be the big boy and take charge of the project. Will it be really expensive? Yes, but look at how much the space shuttle program cost us. By 2008 the bill was about US$170 billion without inflation, which would cover up through STS-126 (there were a total of 135 missions flown). The vehicle was prohibitively expensive, despite being "reusable" because it required about $1.5 billion to refit and refuel it. Rockets are one-shot deals. This would be a reusable space launch system, with minimal fuel requirements compared to conventional methods. I'm confident it would be like putting solar panels on your house - seem's really expensive until a few years down the road when they've "paid for themselves". I think we see space elevators in science fiction a lot not just because they're a technological marvel, but because they bring a new level of practicality to space travel. Springboarding to the Moon, Mars, and beyond. Best plan