The problem is obviously all those doorways. However, I would ignore them in terms of placing furniture and put a comfortable chair on each side perpendicular to the sofa. As long as the chair is small enough that you can easily get around it it's not going to matter if it partially obstructs the doorway. You want to have a U-shaped configuration so that as many people as possible can watch TV comfortably. You'll also need side table between the couch and the chairs in addition to a coffee table in order to make the room look furnished and so that people can place their coffee cups, dessert plates etc, somewhere. You might want to see if there's enough room on one side to place a small loveseat which can seat one adult and one child to increase seating. I would strongly consider a large area rug to lend some softness and color to this room which has so many openings with the bare windows and three large doorways. This will make the seating area look more finished and cozy rather than just some haphazardly placed furniture. More pillows would also be a good idea to soften the scheme and give it some cohesiveness, with the pillows picking up some of the colors of the rug. Colorful and interesting wall art would be a necessity to finish off this room, with more furniture (bookcases, desks, a secretary etc.) against the walls.

What is your style? I'm no pro. I would put a long sofa or possibly a sofa with ottoman or chaise at the end facing the TV wall. Float the sofa with plenty of room to not block the stairway and for people to walk behind the sofa comfortably. Use a large area rug. Long low console under the TV. Then two chairs flanking the sofa with a large coffee table in front of the sofa and one small accent/side tables at each chair. Something like this below

Obviously the pano lens for realty pix has warped perspective a bit. At least with the TV on the longer wall you could watch from the breakfast nook. As I said above, I would float a sectional in the center of the room with one wing facing the TV on that big wall and the other facing the windows/view. The free standing wall would make a great spot for a tall piece of casegoods like a bookcase or secretary. Are you buying all new furniture or using what you have? Maybe we need to see pix of your stuff that you're contemplating using here.

Here's a more accurate room layout with the dimensions of the room and recessed area for the TV. The very simple website I was using doesn't really let me specify an open archway or change the layout of the walls to reflect the recessed area in the corner with the door, but I don't think it matters much. I'm more concerned with having seating for at least 5 people, not obstructing the window view, and giving everyone a good view of the TV. I was thinking perhaps the chair on the left should be a swivel chair, to allow someone to turn and watch the TV better. I could do without the chair there at all, but would like to have family over on occasion and it would be nice to seat more than 4. Do you guys think this would work?