I definitely am a fan of the idea of doing space exploration in a systematic way. We should build a space station that includes a fuel depot, and use it as the hub of space operations.
I am loathe to just destroy the ISS. It was expensive to get it up there and it should be affordable to keep it going. How hard is it really to just boost it into a higher orbit? If we want to save money we might want to stop having people on board for a while... just turn off the life support and other things, but do keep boosting its orbit to keep it where it is.
We will have a real game-changer once we have a "space pickup truck", a launch vehicle that can take a relatively small amount of cargo to orbit, but can do it affordably and frequently. The biggest problem with the Space Shuttle (aside from the fact that it was only 99% safe) was that it took man-decades of labor after each flight to service an orbiter for the next flight.
SpaceX is really working on the "space pickup truck" idea. Recovering the first-stage booster to be refueled and re-used is part of making launch more affordable.
Additionally I would love to see a mass driver or other sort of "cannon" to fire inert payloads (oxygen, water, fuel, dried food, sturdy electronics) to orbit. I've read about this. The biggest problem is that anything you fire from Earth will return to Earth unless its trajectory can be altered; the two obvious ways to do that are to put jets on the cargo capsules so they can adjust their own trajectory, or to have some sort of cargo capture system (a net? a drone with grabber arms?). I favor the latter because I want the cargo capsules to be as simple and cheap as possible.
Once we have an affordable way to get fuel into orbit, all sorts of things become possible. Make a rugged and simple craft that can shuttle back-and-forth between Earth and the Moon, and Moon visits become dramatically simpler and cheaper. Re-boosting the ISS, re-boosting satellites, launching space probes, all of it becomes much simpler and cheaper. Once you are in orbit you are halfway to anywhere in the solar system.