Do you want to keep it? I too have a fireplace that I don't love, brick.. I have contacted a contractor to take it down. But you would have to replace floors etc.. Could you box it in with sheet rock? Or paint the stone or perhaps cover it with tile. What kind of fireplace are you thinking? Here are the ones I have been thinking about. Your could build up the mantle shelf.

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A Newport Beach, Port Nelson Nantucket Charmer · More Info

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Notice this one they built up the chimney and kept the hearth.

remodel lake house with board/batten built-ins · More Info

Paint it. Follow the "More Info" link for instructions:

How to: Painting the stone fireplace white – Greige Design · More Info

I don't think it looks bad. Take everything off the mantel and hang a nice piece of art.

I wouldn't paint the fireplace but I would paint all of the walls the same color. I think some modern art (or whatever type of art that you like) above the fireplace and losing the accent wall color would look nice.

With your paint color and bit of green in rug, I think you have a natural look going - what's the problem!!?? I jest, but am serious also.... I had this open, and seems this kind could go with yours. It's 24" square:

Chartres Wall Decor, Aged Gray and Beige · More Info

As it is now, couldn't your 'cool' things still go?

Case Study Cylinder Planter With Stand, Pebble, Small · More Info

Here's an eclectic sort of mix - for you? I think it's interesting.

Sitting Area · More Info

As far as the accent wall you are emphasizing the very thing you say that you don't like; the fireplace. I really like the fireplace personally but the different color wall is directing the focus even more so onto the fireplace. I would use that green in accents just not on the wall.

I don't think the fireplace looks dated but I think accent walls can look dated depending on how it is done.

What exactly do you hate about it? Do you have photos of what you'd really like instead?