I’d go with a much larger rug in a light color, and add some punchy throw pillows. Some coordinating art on the wall.

Looks like your area rug is on carpet? If this be true and you feel it is dark and it is a tripping hazard easy fix--remove it! If it were the only soft/warm item under foot I would suggest you move it so the front legs of the couch hold it down. You have a lot of doors and windows to contend with. A side table with lamp in the corner the two couches form would be nice. Other than that a wider angle of the entire room is needed for furniture arrangement suggestions. Instead of the rug I would look at curtain panels to soften, add color and give the place a finished look. Just shades always read 'just moved in' to my eye.

Rugs usually don't work on carpeting for the reasons you listed. It looks great with your sofa/loveseat but just won't work in this apartment. Roll it up and store it or get rid of it. We don't see the wall opposite the sofa in your pictures so not sure if this is possible. Put TV on the wall where mirror is now (get rid of mirror, it's not reflecting anything worth seeing twice). Face sofa to TV. With a young child you probably don't want long curtain panels so try valances for some color (preferably a print not solid color) on the windows. Get rid of the pillows that came with the sofa and get a couple in one of the colors in the valances. OR if the TV cannot be moved at least center the sofa between the 2 windows (still get rid of mirror) and hang the art from TV wall between windows OR switch the sofa and loveseat.

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Thank you all for the input! I made a couple changes based on your feedback such as removing the mirror and the area rug. I dont miss the mirror but I feel like the room is bare and missing something without the rug. attaching a few more pictures that might show more of the room m. Thoughts?

The sofa is currently along the longest wall. Since this is a rental, I can’t mount the TV on the wall.

Centering the sofa betweent the 2 windows is a good idea but then what do I do with the loveseat? leave where it is or move closer to the sofa?

Valences are a good idea but I can’t get past their ”old” style feel - any suggestions for a more modern look?

Can you center couch on that wall and then put love seat sort of on an angle where the lamp is? (Not clear to me from pics, but I think a bit of space between the pieces would make them look more to scale w the room).
A big piece of new art with colors would really help liven it up + coordinating pillows. A big plant could also be nice and a coffee table.
I empathize trying to work w existing stuff in a rental. Not easy sometimes!

I tried angling the love seat but it seems too awkward since the room is so narrow. It’s not shown well in the picture but centering the sofa makes the sofa much too close to the closet on the adjacent wall that it won’t be practical to access. I’m stumped

"I'm stuck with the couches." Therein is your entire problem. You literally have two elephants in the living room. They're too big and there are two of them. What about getting rid of the loveseat and replacing it with two armchairs, up on legs, in a pattern that works with carpeting, rug, and remaining sofa?

If you did this, you could float the sofa to face the far window and that would also open up the other window. Put a small console in a color to the right of that window and a couple low armchairs in the corners or facing the other windows--source the pieces from Craigslist.. This would hugely open up the room because the windows wouldn't be blocked. Check Craigslist for upholstered, small-scale armchairs and put patterned or colorful throws that pull together your grey/beige/wall color palette. Get a round ottoman in a color and with a lid for your child's toys. Or put a bookcase behind the floating sofa with baskets for the toys.

Additionally, the very nice wall color doesn't harmonize well with the carpeting, so that adds to the problem of poor cohesiveness. (Maybe the carpeting and walls go better together in daylight. Next time you post a Dilemma, take pictures from all four corners--four walls and daytime. You didn't offer enough visual information.) Are you allowed to paint? If so, then find a lighter wall color that works better.

More up-to-date valance styles

Relaxed Roman Shade

Faux Roman Shade

I use rugs over carpet to add texture, color and ground the space. The key is that you need a very heavy wool type rug. If you choose not to add a rug back, you can add a coffee table or ottoman to make the area feel complete.