How do I make this wall feel balanced (pic attached)?

Possibly add a shelving unit or piece of furniture to the left side of the fireplace that is about the same size/height as the door to the doggie room.

A long, thin bookcase, mirror, or picture grouping to the left of the fireplace.

.Hello there,

Replicate the door and frame only use mirror instead of glass.

Since the hallway door on the left is SO close to the TV wall, I wouldn't add anything there that sits on the floor. That said, depending on what color you paint the wall, the windowed door on the right may not stand out so much because that deep-color-to-white will be a softer transition. You can also soften the door with a lace or gauzy curtain over the panels to mute the light. As for the wall, once the room has it's new floor and paint, re-evaluate the situation. You may like something simple there like a wall hanging. Macrame is coming back and would work beautifully, but you really need to hang something there that fits your style. A built in shelf, as you suggested, would definitely work but it involves busting walls and taking room away from whatever is behind the wall. You've also got wiring going on there. It could get costly as well as messy. Whatever you do, make sure you feel right about the change - you're going to have to live with it every day.

I would paint the door the same color as the wall, or change that wall color, that only emphasizes the unbalance. Have a grouping of something (plates, prints ,etc) over the fireplace and no higher than the door. I say "grouping" because that will engage the eye more than a single piece.

I don't see how you could add shelving in front of the door. I don't think you could recess shelving into an exterior wall. I would close up that door and move it to the yellow wall. Then you could put in the shelving. Otherwise, the only thing I can think of is to paint the entire wall white.

FYI gray is on the way out, finally. The warmer colors are coming back in.