My floor is a neutral carpet over most of the space. It has a little dimension, but it's definitely subtle. It's the lightest one of this pic. Then, we have some tile on the opposite side of the room.

Better picture...

@Calidesign, do you think we could do a Schluter? Or would you recommend something else?

It might be my monitor but carpet looks gold (warm color) and tile look more on cool side of color wheel. Have you looked at polished stone choices for wall? The long planks are more expensive and the space means tiler will be cutting these. Have you considered vertical layout for tile. That would visually lift look of ceiling and be more modern looking. I will hunt for some examples for your consideration.

You're right that the carpet is warmer and the tile is more cool. I hadn't thought of that. I thought about vertical but someone told me since I have a linear fireplace I shouldn't do that. Any examples would be greatly appreciated. I feel like I've been able to confidently make other decisions but this has been harder. I also still have time to change my floor tile choice if it's too cool.

Sarah yes carpet needs to be more gray or gray tile will make it look yellow.

Here is combo of vertical accent tripe with accent tile and horizontal wide but long tiles. Might be good in your area since the ceiling is pretty low. Here is another example of using both accent and gray tile Notice flooring is gray in first picture. I would definitely go with a carpet similar to tile you pick. Very critical to Modern ethos. This is cream look tile, but notice the vertical and accent strip. I would consider that approach. Or leave out accent and just do the gray. I am not a fan of the "wood look" tiles because they are in trend and they will go out in next 3-5 years and then you will have a "dated" fireplace. I would go with more streamlined, plain look that stands the test of time. Also, since your ceiling is low in this area, the more monochromatic the more your ceiling will recede from view. Does that make sense.

I like the tile in the middle with the horizontal lines. Also I would switch the carpet color to maybe the one to the left of it. I wouldn't use the creamy color.

Go to Emser's tile website and look up "porcelain, then Chronicle, then you can check out some grays that might work for you and give you examples to take to your tile supplier. Hope this helps. On your carpet sample board, there is a color in the first one you posted that is just peaking out from the upper left corner. That might be a more gray look in this same carpet style. Check that out. But in any case, get the carpet and tile both in cool look. You will be happy you did. I will keep looking for something I think would be better for you.

We did our fireplace wall with 24"x24" tile, accented with mosaic, to reduce cuts; metal schluter.
We love the look

I love the Chronicle tile. I also like the idea of a vertical accent. I think all the color choices in this carpet are warm so I'm going to see if I can make a better choice tomorrow. I'm pretty bummed b/c I love that carpet, but am so grateful for the amazing advice. Thank you for saving my basement!

You are welcome! Here are a couple more pictures I found that might spark your creativity for your space.

This is verticals similar I think to what Jeff Jones commented on that they did.Here is another concept with low ceiling I thought you might like to see.You could also do a "stacked stone" approach. You don't have that much space to cover so might be worth pricing just to see what the comparison is. Last one, nice long lines. You might be able to do a long hearth to accentuate the long lines? But, glad we caught that carpet thing now! You would have flipped when you saw that. I'm not sure if you want all carpet, but stained concrete is also a great solution for basement floors and you can always get a piece of carpet and have it trimmed to the exact size you want. With a basement, it might be a choice to consider? There is also a website www.flor.com that has carpet tiles that are really nice and pretty price competitive and you can design your floor in many ways and easy to replace or clean one if there is an "accident". Check that out.

Our fireplace wall

@JeffJones. I like how you continued the mosaic onto the hearth.

@FloMangan I like that first pic a lot! I've also thought that stacked stone is too on trend. Is that something you see or am I wrong? Because I really like the stacked stone look every time I see it.

I like the stacked stone but for your more modern look I think a smoother, stone might be better. The stacked is more transitional. Just wanted to give you options.