I believe that the speed of light is so fast that it would be very difficult for humans to maneuver it, because although the time inside the ship is slower, this does not mean that the time outside the ship changes.
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I think the real question here is more about what mechanism or technology would be used to get to the speed of light (or at least close to it). It'll have to be something we haven't invented yet.
Accelerating using a reaction mass carried onboard is unlikely to work, because the mass required (even with nuclear or plasma drives) is just too large, even before we consider deceleration and manoeuvring. A ram drive might work better, but in order to pick up enough interstellar gas and dust to provide the required reaction mass, the ram scoops would have to have diameters like the orbit of a planet.
Assuming we could solve the problem of acceleration and deceleration using some drive system efficient enough to be workable, I don't see any reason why ships couldn't manoeuvre. It would be highly energy intensive; assuming we aren't using magic as a means of propulsion, the energy required to change course would increase as a square of the velocity. But are you sure about time dilation making events inside the ship seem slower ? I thought it was the other way around, that from the perspective of the ship's crew the change in course would seem quite normal, but relativistic effects mean an external observer might have to watch for decades to see even a small change in direction.
The real problem however, wouldn't be steering the ship, it would be shielding it. Unless the means of propulsion induced some kind of "wavefront" ahead of the ship, space debris (particularly close to star systems) could be deadly. Even a grain of dust hitting at a relativistic velocity is going to make quite a mess ! At non-relativistic speeds, e=1/2mv<sup>2</sup>, which still makes a mess if you're travelling fast, while at relativistic speeds good old e=mc<sup>2</sup> means that a rock the size of a melon hitting a ship is going to release the energy of a nuclear weapon. Finding a way to shield from that would be a challenge, but it would probably be too unpredictable and difficult to harness as a source of energy for propulsion.
Quantum entangled wormholes look increasingly safe and attractive as ways of getting from A to B fast. Shame they need so much energy to make them on anything larger than an atomic scale !