I should first say that I have no degrees beyond a high school diploma. I have no training, no associations, and no experience, that would make me specially qualified to say anything. I'm just writing how I feel and from my own imagination.
The short answer is, yes, we will time travel. Of course the nature of Time Travel depends on your definition of it. Is it so simple as just popping back and forth to different times? is it more of a metaphysical concept? if you crush a butterfly are we all screwed?
Through recent experiments we've confirmed that time travel is indeed possible, but for now to a point. But I think if the technology is pushed, it may take decades or even centuries and a number of leaps and discoveries, than actual time travel will become an inevitability;
Energetic; We become able to detect and identify various forms of energy from other time periods.
Audible; Moving forward we are able to tune into the broadcast signals of other times and listen to events. This will eventually lead to listening in on sounds outside of artificial broadcast.
Visual; Focusing in on observation, we find a way to receive broadcasts of visual mediums.
3rd Person; We gain a stationary, window into the past, or even the future, through some sort of means. And view it as we would a TV show. From our singular screen we can observe events as they unfold. In time this technology develops and we can alternate between multiple views.
1st Person; We move forward allowing our view to be that of a specific individual. We experience the time period through their life, but still we cannot interact.
Dimensional; We can now project ourselves into a time period. Though we still cannot physically interact with the world around us, and cannot be seen by the inhabitants of the time, we may move freely and explore as we will.
Atomic; We are able to create an atomic replicant of a time explorer, who may move about the world and more importantly, interact. Once exploration is complete the replicant would than cease to exist.
Navigational; Not satisfied with atomic replicants, we design a machine that may be able to carry passengers through time itself opening doorways and jumping back and forth.
Of course these are just ideas in a shallow attempt to achieve what authors have been writing about for years and years. Reality may actually be much simpler than anything dreamt up. As we know the faster you go the less time passes. And as you approach the speed of light even more so. If you travel faster than the speed of light than the effect is even more profound. If you travel to the nearest star at faster than the speed of light time will have very little effect on you. But in that travel, enormous amounts of time have passed on Earth. You would return to a world nothing like you left it. But than again, when you ask someone what their definition of time travel is, that's not what comes to their mind. They'll want to go back and forth and that's where it, ironically enough, is going to take time. But I do think we'll get there.