General guidelines would suggest seating that faces your fireplace/architectural focal point of the space. I encourage you to put the TV on that wall too. You may have to open a space inside the bookcase for it and have wiring installed, but you'll get TV out of the traffic path from the front door. I assume there is a matching bookcase left of the FP. That's where I'd put the TV, away from window glare. More photos of the missing walls would help get the room arranged so that an appropriate rug could be suggested. Comment and use the Photo button to upload pix.

Agree with above but if leaving set up as is I would definitely get one wider than the 2 chairs and start it about 1 foot from the FP to under the TV console

Make the rug as large as possible; that makes the room look larger and also much more welcoming. A large, colorful Oriental rug would look great here. I agree that the placing of the chairs and TV is awkward, and the TV should be on the opposite wall. I would get another couch facing the fireplace and TV. These chairs just don't look right in this room; they're too large and ponderous. You have a nice room which at the moment isn't living up to its potential. The right rug will go a long way toward fixing that.

following

Thanks to all!! We are going to go with Beverly’s suggestion! Much appreciated.

Could you humor us and jiggle that arrangem before you finalize a rug?

Costs zero to try

We have a very similar room and set up. In 19 years I have tried everything except the TV over the fireplace because the fireplace is on a raised hearth which would put our TV behind the cedar beams at 8 feet. Only a month ago I had a carpet remnant turned into an 8x 10 foot area rug and placed it between the TV and half way under the 2 recliners. It seems to work well. And the dogs like laying and wrestling on it. We haven't used the fireplace in years so it doesn't bother us that it's behind us. I think going with Beverly's idea will work out fine for you.

It might be nice to try a new arrangement for the room since you have the backs of the chairs to the fireplace. Is there room to place the TV to the left of the fireplace? Then you could add the sofa facing the TV/fireplace and have the chairs where the sofa is now. Note the arrangement below:

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