I have a 2001 Toyota Echo which developed severe vibration feeback to the steering wheel when the car was driven at low speed or stopped at a trafffic sign or signal.
I took the car to the Toyota dealer and they checked the brakes, replaced the front rotors. They also checked the fuel pump and other engine components. The spark plugs and PCV vale were replaced, as well as the crank seal.
When I left the garage, the vibration reappeared after driving about five minutes. I immediately went back to the garage and waited while the mechanic checked the car. He came to the waiting room and said I would not believe what they found. I went to the garage with him and the hood on the car was raised. He started the car and there was no unusual vibration. He closed the hood and the vibration started again. The problem was that the underhood reinforcement panel had come unwelded (or unglued) and it was vibrating. A mechanic came from the body shop and put a sealer/filler at the loose spots, we let the car sit for a while, the mechanic said the sealer/filler would expand to close the gap, and I drove the car home. The vibration had stopped.
While it was a good idea to have the brakes checked, etc., that could probably have waited awhile.