Do you have any photos of the space?

ETA: My first thought, without photos or knowing where doors lead, would be to angle the rug. It solves the issue of it not being centered and the tripping hazard. Then center the sofa on the wall. (Excuse my terrible phone rendering.)

Here are two angles of the living room with the rug situated centered to the back wall. Hopefully between the rough schematics and the pictures commentators will understand the dilemma. Please ignore all art, paint colors, window treatments, etc. We are attending to everything, eventually. Need help with the rug placement and furniture layout. Thank you.

To be honest, I can't see myself doing either of these things as it makes my head spin. Once the rug is anchored somewhere in the room at right angles, I was hoping to deal with the symmetry/balance issues through furniture placement/layout. Keep in mind, the sofa is not the only piece of furniture we will be adding to the room.

Interesting, smitrovich. There is the wall between the entryway and the door to deal with. That's a lot of blank space and how do you contend with aligning whatever is on that wall to the fireplace (and the furniture grouping?

I like smitrovich's layout. As to the blank wall, cheat it a bit. Put a console opposite the fireplace, then put something else to the side of it (plant possibly) to make the pair look centered on the wall. So, console centered on fireplace and overall arrangement centered on the wall.

I don't see that as blank space, I see it as an opportunity to hang art, a mirror, family photographs, create a gallery wall, et cetera. There is already enough symmetry in the room. You can get creative with that wall.

Thanks. What other elements need to be added to the room? I think I like this layout, but would appreciate contrasting ideas as well.

I like the layout posted by smitrovich. You can also add a slim console under the paintings..one that is longer than the span of the two paintings. You could add one or two lamps on that console as well

What else do you want the room to do? For example, if a TV needs to go in here, that changes the calculus a bit. Or if you'd rather get a little desk off to one side, etc. Otherwise the arrangement that smitrovich posted is the best for conversational use of the room, while if you want mainly to sit and watch the fire, you could turn the whole thing 90 degrees, with couch just off the lower wall, chairs facing it, to either side of fireplace (with a side table by at least one, with a reading lamp). I honestly think you're overthinking the difficulties of the very small offset. Just split the difference between perfect wall alignment and perfect fireplace alignment and get on with your life.

No other use other than conversation with guests, watching the fireplace, etc. We have a family room with a TV. I was thinking more about the corners of the room, the 3 anyway, by windows and what to do with those empty spaces. As for overthinking the offset, my initial inclination was to orient 90 degrees as you say with the couch facing the fireplace. However the offset is large enough to bother me, so compromising and moving on is not an easy ask.

The layout proposed by Smitrovich is the best, because the area between the entry and the other doors is basically a path of travel and you don't want any furniture obstructing it. You could reverse it by placing the sofa on the left and the chairs on the right. There is no need to keep everything symmetrical. If the fireplace is the focal point, dress up your window treatments to reflect the design and colors of the rug. It will expand the importance of that wall. Place a mirror over the fireplace to reflect the opposite large wall which you can use as an art gallery with track lighting (secondary focal point to balance the room). But leave it furniture free for ease of travel.

Thanks everyone for the feedback.

Can I ask what you did in the end?? I’m having the same issue however if I go with the suggested layout with the sofa on the right it sits under a window which I would have preferred to look out of while sitting on the sofa facing the fireplace . I have one entryway on the left which is knocking everything off centre. Very annoying. Would love to know what you went with!

Can you send a photo?