If one could travel at the speed of light which I understand the current laws of physics say you cannot wouldn't you travel to the future?
Yes and no. You wouldn't really be "traveling to the future" as much as you would be compressing time. That is, you are, right now in this moment, "traveling to the future" in the same way you describe. This would be more of an acceleration through time, which is absolutely possible.
It would be effectively the same, except that you would still experience the passage of time. So if there was some kind of coefficient of real-time compression to travel to the future, there would be a limit how far you could go based on the length of time you have left to live.
We generally think of the time travel fantasy in instantaneous terms. i.e. I step in a time machine, punch in a date, press a button, and I'm there (within lets say a Planck time). What you're describing would still get you to the future, but it would be limited.
So yes, you can accelerate through time, but you cant jump to "the future" instantaneously. To do that would require precise coordinates in a hypothetical quantum physics matrix which would define the 3-dimensional position of every particle in existence, which we're not gonna get.
Good question, btw.