If I leave my car sitting for longer than approx. 24 hrs, and I start it up and start driving, I can feel something vibrating/shaking subtly in the front area of my car (as if it were coming from the wheels or axle or engine). But then after ~5 mins of driving, it completely disappears and everything is back to being smooth.

Any ideas what's going on here?

 

"Flat spots" in the tires form when the car is parked and the tires cool down. Driving warms the tires up - the belts in the tires get more flexible and the vibration disappears.