Looks like you have an embarrassment of riches--many people struggle with rooms that have no focal point, and you have two! And you don't have multiple doors, which make for awkward traffic flows, so that's another positive.

How is this room used--by adults or children or both? Is it the main living area for a family with kids or is it a quiet adult retreat? Is it used for entertaining and if so, what kind? Is there a TV in the room? How many people do you need seating for, both daily and for entertaining?

For starters, I'd say pick one focal point and build the room around that. If you have a nice view out the bay window, that could be your focal point, with a smaller seating area near the fireplace for a reading nook.

But in large part, the furniture and where it is placed depends on how you use the room.

Do the windows in the bay go to the floor? If not, how much space b/w the floor and the bottom of the windows? (Just wondering if that's something you would put furniture in front of, or keep it open.)

I was also wondering about the bay window. Is that to the ground or does it have a window ledge? If there is a ledge, how far off the ground is it and how deep is it? Is it close enough to that floor that you could put a cushion on it and use it as a little window seat for kids? I did this in my current home.
Also, more about how you use the room and what room you enter into it from will help. Pictures of the room are helpful too.

Unless you have a great view the window focal point is from the door as you are walking in and not necessarily one for the room. The natural focal point of the interior is the fireplace. The real issue is if you have to have a TV in here or not. Post some pictures of the existing room so we can see it in 3-D.

Today on the Nate show, he put a round table flanked by two chairs in the bay window. He said it doesn't have to be the focal point. His layout looked very good. If you did something similar, you could put the sofa in front of the small window with a console table behind it.

Wow. Ya'll are great. And quick. Thanks so much.
Okay so the room is really the only living space in our rather "efficient" home in NYC. That's code for, I can't move any walls.

It is directly off the entry way ("foyer") with the dining room across the hall.
I would like to figure out a way to put a TV in it in a hidden unit somewhere but the first requirement is really that it be set up to entertain guests comfortably with plenty of seating without looking too cluttered. We don't have children, but our friends and family do.

The window sill in the bay is 27" from the floor with a radiator below it (the house was built in the 30s and we have not successfully found room for HVAC ductwork without losing much needed space. This also means that there is a really "lovely" a/c unit built into the wall to the left of the small window, yuck.
The sill is 14" deep at the back (to accomodate the radiator) but only 4" deep at the sides. The measurements I've provided in the layout are for the floor space.

I wanted to avoid pics because the space is truly a mish mash of furniture right now (not to mention the ferns that are overwintering in the room right now)

As a further note right now, the sofa in the room is either going, or will be reupholstered in an off white fabric and the oversized chairs, I think should go as they seem way too big for the space. Again, assume a blank canvas.

I tried putting the sofa in front of the small window with a console table behind it, which I could try again, but it seemed to push the rest of the room too far in front of the bay window/ left little room for additional seating.

to enlarge click on the thumbnail

Oh yeah... of course the rug situation is a complete mystery to me. Did I mention I did not get the decorating gene? ;-)

Thanks again.

Try this:

The sofa on the wall with the small window, but no table behind it and a coffee table/ottoman in front,

The arm chairs where they are now.

A small game table and four lightweight chairs around it in the bay window.

The TV on the wall now occupied by the sofa, and mounted on either a swing arm or a rotating stand, if needed to make the TV more visible to the people on the sofa.

This gives you seating for at least 9 people.

Alternatively, keep the sofa on its current wall and put the TV on an angle in the corner between the two window walls

Your basic room really seems pretty charming. If it were mine, though... :) I'm actually wondering if there's a way to make your arrangement problem worse by adding another doorway! Seriously, for us, the room would work so much better as a natural magnet at the center of our home if traffic naturally circulated through it, instead of it being a dead end off to one side. Another doorway?

I would probably try something like: (Starting at wall to left of doorway and continuing clockwise:

End table (lamp)
Sofa about where you have it(coffee table in front)
Substantial corner table (lamp)
Two upholstered chairs on end window wall.
Game table and chairs in bay window, as suggested.

Two chairs facing each other with an ottoman between them in front of the fireplace with a floor lamp (or sconces) added in this area, and a small lightweight table to service each chair.

I forgot about the TV. I might try to put one in the left hand niche or do it the old fashioned way and have it on a mobile table that could be moved out. An articulating arm just seems too modern for that room (which is a very nice room by the way. I was expecting a nightmare from your title)

Thanks so much ya'll for all the great recommendations. I am quite certain that I will struggle with the size and composition of the items and need more help but will come back soon.
First things first I guess I need to rehab my sofa and few other items.
be back soon!

I am in love with your fireplace and built in shelves. So graceful. I do think you are right the chairs are too big for that space. Other than that I will leave it to Pal and the others.