I think that we're far too technologically immature at the moment to even contemplate the mysteries of covering vast distances in space. We are obliged (forced) to think of 'speed' within the parametors of what we know so far, because we have no other 'mental' solution (ability) as yet. But, just like discovering that the Earth is not really flat and that we can travell on a train (RLS's "Rocket") faster than the speed of walking without suffocating, we will, I feel sure, as our knowledge widens, eventually discover, how to get from one solar system or galaxy to another, with ease, at, say, for example, the equivalent to the speed of thought.
I realise what I said above is a massive stretch of the immagination, I can't really believe it myself (no more than I can conceive what's beyond the universe), but I base my suggestion on the natural progress of the human race, and with all that space and billions of other planets out there to explore, there just has to be a way for us to explore them (as we are pobably being explored right now, by much older and unbelievably adavnced beings from other planets, who's ability to visit us without being (fully) detected, is as equally incomprehesible to us at the moment, as their ability to move at such great 'speed' (as we think of it) over such vast distances).
So, my answer to your question (totally unfeasible as it sounds at this moment of our comprehension of all things possible), is that one day, in my opinion, we WILL (because we MUST) be able to 'travel(?)' even 'faster' than the speed of light.