Can you travel at infinity miles per hour? Well, infinity isn't really a number so, probably not. But how fast could, we'll say a person, travel? I would say the speed of light is the fastest possibility, but let's start out a bit more realistic. Usain Bolt can run at 28 mph, but this is physics, so 12.5 m/s. Not a bad start. How about something faster, the fastest train is the Maglev, at 120 m/s. The fastest land vehicle - Thrust SSC at 341 m/s. The fastest speed by a manned vehicle was the Apollo 10 at 11082 m/s, but that's still only about 0.0037% the speed of light. But wait, we're on the Earth, aren't we, and that's moving fast, about 30000 m/s. And now that we've considered that, how fast is the milky way galaxy moving? 581152 m/s! That's 0.19% the speed of light. I don't think that it is reasonable that people will get close to traveling faster than our galaxy, at least any time soon, so guess it's time to give up.
But, let's consider something, could we already be traveling at the speed of light? Here's the idea: there is a person at point A standing still, and a car moving at 16 m/s, and there is a point in the car, point B, where relative to that point, the car is not moving (kind of like how relative to us, the Earth is not moving, but relative to the Sun, it is moving quite fast). So, from that point B in the car (if you can imagine) the person standing at point A is moving, relative to you being still, at 16 m/s.
So, considering this example of relativity, can we say that relative to a photon, we are moving at the speed of light? Yes. Wait! No, no, no that can't be, we did not consider something, I said there was a relative point B where the car was not moving, so there would have to be a point where, relatively, a photon is standing still, and that is not possible in any reference frame. (Also technically there is no reference frame where anything but a photon can be moving at the speed of light) - but we still went through with this thought procedure in light of that... get it?