What about painting the brick?

I was also going to suggest painting the brick. I think it would look great if the red was toned down to more of a brownish-red. I like the brass w/glass doors and the general brick pattern of the fireplace.

The quickest, easiest, and cheapest thing to do would be to paint it. That would be my first step. If you hate it, you've only wasted the cost of paint. And you don't have to choose white!

Before you paint it all the way, try a whitewash to tone down the red. We whitewashed ours and my husband wanted to stop there, but the peach/pink was still prominent for my taste so we painted it white. I would have loved it though if our brick was red.

before i would paint the brick I would absolutely paint the walls a darker color--the stark white walls against the wood tones of the mantle and the red brick is too much! Paint the walls, accessorize--then if the brick is still a problem I'd deal with it.

There is something odd about the brick overhang that is wider than the firebox opening. Before I did anything, I would at least remove the two end bricks that are overhanging by so much. Then I'd paint. I agree the white walls are not the most flattering.

I would also consider painting the brass surround with black high temperature paint.

I would choose 2- 3 colors in the warm family( cream, beige, and a brick, or colors that you like). I would water down the paint and gently sponge/drag it over the brick to give it like a new but tri color. You don't have to be precise. Just a little dab here and there may do the trick. Change the insert or paint it to black. Paint the mantel white or a color that goes with the 3 colors that you choose. All this also depends on the paint color on the wall and the items in the room.
If you don't like the effect from the 3 colors, you can always paint it over with full strength one color paint. One color Whitewash is pretty, too.

I would draw the FP with the existing color on paper and try the 3 colors on a piece of paper to see if doing each brick with the 3 colors is a good idea, or each color per brick, or a combo. Play with it. Decide what YOU like.

I love real brick, so I would never totally paint it unless I couldn't find a better way to perk it up while keeping it fairly natural. Brick FP are very cozy and charming. All many of them need is a little pick-me-up.

I also had an ugly brick fireplace with an even uglier mantel. I ended up replacing the mantel and had new tile put over the old bricks. It looks like a brand new fireplace now.

I would try whitewashing the bricks first. I agree with Annie; I would remove the bricks that are overhanging. Most likely there are bricks underneath. As far as tiling over the brick; I'm pretty sure you can do that if you want to. But would the tile stick out too far past the mantel if you did that? Is inching out the mantel an option or is it stuck where it is? Because you'll want to consider the depth if you add mortar and tile on top of the brick. You could also put thin stone over the brick instead of tile, if there's space.

I agree with painting the walls as others have suggested. Once you decide what you are doing with the brick, you can use that as a starting place for paint color inspiration.

Another idea is to paint the mantel a color that would go better with the existing brick.

BTW, although you may wish to paint them first, it is possible to tile over brick (or put a slab on it). But I think it would not be worthwhile unless you removed that course of bricks that extends beyond the mantel face. You then have a bed of mortar floating on the bricks. What is the rest of the home like? Is the brick more appropriate?