2004 Chevy Silverado Truck vibrates

My truck seems to vibrate when it is going anything but slow (maybe over 35 MPH?). I can't tell if it's coming from the front or back and it isn't extreme, just enough for me to notice it on an otherwise-smooth road. I just checked my tire pressure and one was fairly low, but I filled it up and drove it right after. That didn't solve the problem. My tread is fairly low (probably only a couple mm's from needing replacing).

Any suggestions on what is causing this? Or, even better, an economical/efficient "process of elimination" I can follow to try to locate the problem?

Thanks.