There are a few questions regarding the Alcubierre drive here, so I'll pose this one and see what I get.
Currently, our space exploration vehicles, both manned and unmanned, are at the mercy of Kepler and Newton. We have some control over what direction we're pointed and how fast we're going, but our movement through space is governed by slingshotting around the Earth, Sun and other planets and moons, which allow us to gain, lose or maintain our velocity much more efficiently than any rocket could. There's no energy source nor thrust motor we can conceive of that's powerful or long-lived enough to allow us to ignore orbital motion and simply push, against the Sun and any other nearby gravity wells, to take a relatively straight-line path anywhere in our neighborhood.
Editing based on Deer Hunter's comment...
Let's now conceive of a drive system powerful enough that we no longer need to use gravity slingshotting as our primary means of propulsion outside LEO. The Alcubierre Drive is currently the most plausible future tech, but we could imagine virtually any drive system that would allow us to not only "win", handily, against the straight-line pull of anything in the Solar system, but be efficient enough that such a tug-o-war is a drop in the bucket for the fuel capacity of the ship equipped with such a drive. Such a drive system, even if it were subluminal, would be the gateway to the solar system (even half-light speed, impractical for interstellar travel, would make landing on Mars and coming back a day trip).
Here's the question; given a drive system, Alcubierre-based or otherwise, powerful enough that we no longer depend on gravity-based navigation maneuvers to get around, what role would gravity still play in our navigation and maneuvering? Obviously, where gravity helps us out, such as falling toward the Sun to cross the system, we could let it, and there's really no "standing still" (though even that could be possible with such a drive system, depending on your definition of "still"), but given that we'd have the ability to travel much faster than gravity could pull us, I imagine that gravity would be more hindrance than help; we'd simply adjust course to account for the effect of gravity wells as we pass by them, much as we currently do in airplanes to account for wind.
So, would gravity really matter anymore in the post-reactionary thrust engine era of space travel? Or would it, much like the wind to an airplane, simply be something to correct for?