There are a number of high-startup-cost, low-running-cost schemes for putting stuff in LEO, and as someone once said, LEO is halfway to anywhere in the solar system, energy-wise. Some possibilities are laser launching, space elevators, launch loops, and electromagnetic guns.

Some of these have much higher startup costs (to be effective for human launching, a gun would have to be very, very long and possibly cost the most of any of these, but shorter ones could launch material at very high acceleration with much less up-front cost), and some of them have awful failure modes (the space elevator could spread destruction in a narrow path wrapped all the way around the earth if it failed in the wrong way, via separation from the counterweight), but they're feasible.

The cheapest ways of getting to orbit, therefore, approach the cost in electricity of the task, which is less than 10 KwH per kilogram, or about $2USD per kilo. A recent flight from coast to coast cost more than that for me.