Certain tire makes can give vibration, I have just got new front tires and I too used to get vibration just like you at 60pmh. My old tires were fine. I fixed the vibration today as i noticed my steering damper had a leak underneath car. I bought new one for £25, and it only took 10mins to fit, 2 bolts. The old damper moved easy, whereas the new one was nice and firm. Vibration now gone!