this could have MANY answers, but the most common is worn out brake pads rubbing against the rotors.
97 grand am rubbing/grinding noise from right front that is not wheelbearing or brakes
rack and pinion
The grinding noise is the brakes pads proably the noise is in the front. The front brake pads are easy to replace and is a do it yourself sort of thing. My guess is your brake light is coming on because of this condition. I assume your brake light has been coming on for a little while now.
Failing strut, cv joint or steering bushing.
No, there should not be any noise. Sounds like something is not properly fitted.
The problem is probably the rear wheel bearings
I had a noise in the front end of my 2004 Mountaineer similar to what you described and it was front wheel bearings on the passenger side. $291.
camshaft dephaser pulley
Grinding - 2004 was released on: USA: 18 August 2004 (Angelika's New Filmmaker Series)
Depending on what is causing the problem, it can cost between $10 and $300. It depends on the problem and the cost of the parts, and labor.
The cast of Grinding - 2004 includes: David Matranga as Gunter Weaver
I have a 2006 XL1200R that intermittently does the same thing (I'm wondering if it has something to do with primary chain tension).