You are wise to address this. I would recommend painting this the color of the trim (baseboards & moulding) in the room and replacing or repairing the mantle along with getting a nice fire screen. This is most likely the focal point in the room. You will have to speak to one of the professionals at the paint store to get the details on how best to paint the brick as it may not be the easiest task. But from the photo cleaning does not look like a easy solution.
Good luck!
"There's never a second chance to make a first impression!"