The TV definitely doesn't need to go above the fireplace, so put it on the wall where the art is. The you can get a rectangular table or a round table.

more pics to show what's on the other side of the wall. powder room, pantry kitchen and dining room kitchen is almost done

This is such a pretty room!! Omg love! Anyways. I agree. The current light you have needs to have the table under it. Either we can swap the light or just move the table. I also think your not satisfied with the current because the couch is blocking rounded bay windows. So it looks a bit strange. Again,that’s why the table would help if it was there. If the couch is on the FP side of the room I’d face it the other way than from the picture shown meaning facing the porch doors and FP. also, when and if you move things around make sure the couch is on the rug.... you have very nice furniture and a beautiful space!! Love it and totally see the vision

Samantha a 60’s home is fun. im not a designer or decorator but whats important to one person may not be to you! i hate everything shoved up against walls! but you may like that, don’t know! are you a tv and movie watcher, do you exercise with your tv, how much of a part of your familys life does the tv play? do the kids watch it a lot and do you depend on it to keep the kids calm for a while? do you like to louge with your feet up or sit with your feet on the floor? all this matters! making an entire room into a play room can keep clutter out of your main living space however you have no line of sight into that room so that may make you a nervous reck. id be looking at knocking down the walls and getting rid of that small galley kitchen but then im a cook and i have big big family dinners. but a small low cost project would be to create a small pass-through or bar/counter to that family room from the little kitchen nook you are showing there. your negitives are that you have no outlets except on walls and no overhead lights and with kids you dont want cords strung around. now a way to get around that (or mitigate it) is use an area rug, buy a flat (not standard round) extension cord and run it under the rug. then you can setup a sectional in the middle of the room with a chaise facing your tv and the other side facing the bowed window. this will give you light and end tables next to where you are sitting (likewise you could do runners as theyre cheaper than a carpet or area rug, to form a sudo walkway and run cords under that.) then nothing is blocking the window nor blocking the fireplace or multiple entries to the room. if you were to knock down the walls on the little kitchen you could move the dining to that family room and also create a corner breakfast nook and bar. however if youre more of a movie buff family, then that back room would be a perfect movie theater. you could create a step up platform and 2-3 rows of seating the place a big 85 inch tv on the wall. that would leave your living room more of a gathering room (no tv) for socialization. if you like cards, pool or other things you can concider that in your gathering room. point is think about the top things youd love to do and the top thing you cant live without and design your interior of your home for that! its yours! also think about things you hate and make sure you avoid those! if your laundry isnt on the main floor and you hate running up and down stairs then maybe look at a space for that, if you hate vacuuming look at no carpet…get the picture. If you find you can live with things then we’ll call that an interim plan, but make sure it doesnt get in the way of your ultimate goal. example: if you love gazing outside while doing dishes or watching your kids play while cooking, dont remove windows to make more cabinet space! adding windows later will be expensive and require a structural engineer! make sense! i hope this gave you ideas. the one big thing i see or rather dont see is storage! really think about “is there a place for everything you own?”… winter, summer, fall, spring, holidays, etc… homes from the 60’s lack this and thus if youre a neat freak not having the ability to put everthing away may make you crazy! as you get older you accumulate things which are seasonal.. think about it!