Right corner for the TV away from window reflections.

Why do you have so many couches? are they all needed? If not then take away the patterned one and push the other three forward a couple of feet. A more "out of the box" idea is to mount your tv in the left corner about the same height as the fire place mantel. I have no idea what to do with your floors, its really unique!

TOO many couches, look like furniture store not a hose. unseals u have a family of 10, u don't need them. a nice sectional will do. and leave the window unblocked. u can put plants on both sides of it
i would also hang long mirrors on both sides of the fireplace.

I also would suggest not mounting the TV over the mantel, except that you gave a legitimate reason for doing so: to watch from the kitchen. I wouldn't mount it in the corner because it will be hard to balance the wall.

I agree that the patterned couch either needs to go, or be recovered in something more modern and used to replace one of the other sofas. Your seating is very matchy-matchy which usually results in a room that lacks interest and personality (and reflects a well-trained salesperson).

I would remove the sconces altogether. Instead, I would get identical tables or cabinets for both sides of the fireplace. One can hold your components, the other will be a good place to stash the clutter that accumulates and disrupts the space. Style the top of each cabinet with a lamp and some art. Make them balanced, but not matching.

Pull the furniture away from the walls. Since you won't have a rug, I presume, add color with pillows and curtains.

Identical cabinets:

The shiny patterned floor reminds me of a basketball court, so I'd be desperate to cover it with an area rug if possible. Take the print sofa to the master bedroom if you have room, or sell it on Craig's List, along with the Queen Ann coffee and side tables. Make the most of your ivory contemporary pieces by adding complimentary tables in glass and chrome. Colored print drapes over textured fiber shades will take this from builder's special to a more custom look.