Sounds like it probably just needs new rotors. Usually this type of shimmy is caused by warped rotors. Plan on a brake job - new pads/rotors. You can pull a wheel off and see how much rotor and pad is left. If you do the work yourself then you can probably get by with less than $200 for parts. I don't know what it would cost to pay to have the work done.
You will want to have the wheel bearings repacked while doing the rotors.