2012 Prius C making a strange noise in front passenger tire side.

If it IS the water pump and it fails completely, that can be hard on the engine.

Get a 3rd opinion, maybe after driving it a while longer.
In today's market, $560 really isn't that bad for doing the pump and
replacing the coolant.

 

if it's that faint, ignore it

 

If it gets louder as you speed up and seems to go away after 50 mph it could be a wheel bearing. Often will be quiet for the first ten minutes in the morning.

Sometimes the side of a droning bearing will be mistaken. An experienced mechanic will recognize the sound on a test drive.

Edit:
After listening to the sound file it might be a rubbing brake backing plate which could have been tweaked some after the mechanic looked at it. Could clear when jacked up.

Sound file (scroll down)
SndUp | Post info

 

LOL

 

Rocks and other debris inside of hub caps can cause a similar problem.
So can metal hub caps that aren't fully seated.

 

This sounds similar to a repair we just had to have repaired which was the passenger side cv boot tear. Also I have read where yes our pads last a long time although the caliper bolts can have wear and rust which can make noise if the caliper is not opening and releasing properly. This we will be having checked with the wheel alignment that we need to get asap. Although we just got the car back yesterday after the car being out of commission for a week now. Our back brakes look rusted to hell and back. I will be posting about them and asking others opinions about them. Hope you find your issues and a solution.