I think a off white rug would be a good idea. Would brighten up the room. And I see you have white furniture pieces on both sides of the fireplace. I would put a tall white bookshelf where that short desk is on the other side. That will help balance out the room and break up that large expanse of wall.

I kind of love this mix of metal coffee table and rustic side table.

Cow Hollow Modern · More Info

Something like this where the small desk is:

Hollow-Core Bookcase, White and Gray · More Info

I like this even more:

Delta Composition Bookcase, Pure White · More Info

This would be a good coffee table to mix in:

Wimberely Retreat · More Info

I would do this over the desk and then a larger piece of art by table.

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Think the best way to break up that blank wall, if you want the desk to stay, is to add a tall plant to the right of the desk and some art above the desk.

How about the art that is shown in photo, placed over the desk, and a plant like this to the right of the desk;

Living room · More Info

I would do window curtains in a color block or geometric pattern as show in picture; divided equally but still giving you a view. Just need to adjust blinds at night for privacy.

Modern Living Room · More Info

Gallery wall of family members professionall matted and framed.

Scenic · More Info

Go big or go home. Paint some soft stripes on wall horizontally in variations of the color on your wall now. Lighter and darker and some white. Or just one single wide white strip with different sized but all framed and matted pictures of a place you have been as a family.

Childs Bedroom · More Info

An architectuaral salvage piece?

Modern · More Info

DIY if you are patient!

BRIDGEWOOD · More Info

Possibilities. Oh and your home is so very relaxing and beautiful and interesting to view. Must be fun to live here!

You have nice shadow effect on the living room wall. That is missing from the opposite wall. You could add some uplight to a plant, and/or a tall thin lamp to the desk.

TA DA:

Kitchen Pocket Door Series 1500SC · More Info

With the white shag in the living room side, you should also add a brighter rug under the dining table.

~5 ft. x 7 ft. Grey Soft Floral Transitional Living Room Area Rug, Hand-Tufted · More Info