If your aim is to draw the conversational feeling of your seating more closely together, to make your interior feel like a special gathering place, I would simply take your dining room rug and put it in the living room -- at least for now. If you want to draw people into the seating with color, just pick your favorite color. Your furnishings are so neutral, hard to imagine what you pick that would clash. An old fashioned '''medalion oriental'' rug might look out of place, but any other kind of pattern that appeals to you should be fine.

BUT

If your idea is to float your space as part of your beautiful and actually enchanting view, then I would study the colors outside your window and decide what you want your carpet colors to be linked to, your favorite aspect you want your room to join up with. I would choose a carpet that you feel harmonizes best to give you that flying carpet feel.

it appears that an 8 x 10 is suitable for the living room.

the dining room rug looks a little tight. is it Navy? are you interested in keeping the rug in gray tones or are you up for some color?

the chairs should be on the rug when pulled away from the table.

Ruggable and rugs.com have many affordable rug options.. https://www.wayfair.com/rugs/pdp/kelly-clarkson-home-power-loom-navycharcoallight-gray-rug-w005363712.html?piid=490182873 

this is a pretty Navy & Charcoal option from Wayfair.com ... under $200.00

I agree with mytwo cents to study the colors outside, and with Lyn Nielson that the dining rug is too small.

The DR rug is too small and I do not like rugs under dining tables usually . s for the LRI like the floors so I would probablt just do a big black and white cowhide uder the coffee table . Get that clock off the wall and replace with a fabulous piece of art and then use colors from tat for some accents

Your clock is one of the rare instances where I think it fits the scene out the window extremely well and makes for a kind of 3-dimensional symbolic link to it. It's like the clock is the near-view of the industrial urbanscape. Again, if you want to enclose the room and down play the view, and keep everyone's focus inside the room, replace the clock with an art piece that stops the eye cold because it has no relation to the view and keeps the focus on the indoor space

https://www.chairish.com/product/2285670/vintage-books-print-on-canvas

If you want to extend the feeling of the space of the room to the great outdoors and make the wall disappear, keep the clock.

I keep looking out your window and wondering if I am looking at the old jewelry district of Providenece RI

If you want to go monochromatic, then

Or if you want some color then bring it

https://www.wayfair.com/rugs/pdp/foundry-select-vanita-transitional-southwestern-fringe-area-rug-w009078113.html

or https://www.westelm.com/products/colca-wool-rug-t1657/

https://www.ikea.com/us/en/p/stockholm-rug-flatwoven-handmade-stripe-black-off-white-90103254/

Try the rug in the dining room, as it is too small for the table/chairs. The rug should be at least 3' larger than the table, all around. Measure so that when the chairs are pulled back they are still on a rug,

Try a chair on the other side of the coffee table. It could look more conducive to conversation. Then measure for a rug so all front feet of chairs/sofa are on it.

If you want color you can certainly have something bolder than brown black and white.

https://www.perigold.com/rugs/pdp/ralph-lauren-home-great-plains-geometric-hand-knotted-wool-area-rug-in-ivorybrownred-ralp1079.html?piid=11102414