Brakes and rotors

If the squeaking occurs during braking, there are a lot of things professionals do during a routine brake job to prevent that, and there are some things do-it-yourselfers can do to cause that. If the squeaking occurs all the time or when driving over bumps and potholes, it is likely to be suspension-related. Your best bet for that is an inspection at a tire and alignment shop. They will look at ball joints, tie rod ends, control arm bushings, anti-sway bar links, etc. If the noise doesn't occur all the time, you can help them by figuring out how to make it occur so they can duplicate it.

One problem that some people are running into is higher-quality brake pads actually squeal more because they have a harder lining material. Sometimes that will stop as they wear in and mate to the microscopic grooves in the rotors, sometimes the noise gets worse. If the noise wasn't there before the recent brake work, be polite but insist they recheck their work. As I mentioned, there are a lot of things they can do to prevent squeals, but sometimes those things are done later when addressing a "comeback". If they can't stop the noise, I can list a few things they can do in case they aren't aware of them already. When I taught Brakes class, we spent a lot of time discussing these things to stop noises.