Rug or art first. Everything is gray now including your floor. Art is personal look at minted.com for ideas

Rugs with color.

Rugs for monochromatic look. Use colorful accessories and art with these

These are "william morris" style wool rugs.

OK so you have selected some very good pieces to start with and the room looks quite nice. However, it's hard to understand how the TV relates to the sofa. The seating arrangement should have at least one lounge chair, may be positioned where the table and chairs are located. Some with your furnishings layout is off.

Many colors will work with gray and white. It doesn't have to be blue, but this was an easy reach. See examples below. All from Rugs-Direct.com

The sofa is perpendicular to the tv. Should I change the artwork if I add a (blue) rug?

I think you'd like a floor lamp near the sofa.

Orbita Arch Floor Lamp, Dimmer, 12W Dimmable LED Bulb Included, Drum Shade, Brus · More Info

How about moving sofa to where table & chairs are so it faces the TV?

Your art appears to be very neutral, and even if it wasn’t, the art does not have to match the space. So regardless of what color rug you decide upon, the existing art is fine.

A rug recommendation for you (ivory, dark brown): https://www.rugs-direct.com/Details/LoloiRugs-Enchant-EN28/124656

ETA: Another rug (Aqua, Dark Brown, Taupe, White):

https://www.rugs-direct.com/Details/Surya-SantaMonica-BlockedOut/132483https://www.rugs-direct.com/Details/Surya-SantaMonica-BlockedOut/132483

Lack of lights and seating furniture. What I like is your blinds. I would move vertical big mirror to the bedroom. I would go with some color that brings some warmness, for rug, then pick some throw pillows, some extra chair and some lamps on side tables or just tripod.

Look for a colorful rug that you really like (trying for a pattern that has a little brown…to tie in with the kitchen cabinets )…then let that be a reference for adding color to you room…i would start with an accent wall …the one behind the tv looks as it it was created to be an accent wall ..such an interesting shape..and angles!…i

So now that you have revealed the rest of the room we see the rug selection must bridge the gap between the gray and white furnishings and the vanilla walls and brown cabinets. This will be more complicated. I have added rugs but then painted your island dry wall a color to help with the link.

The mirror needs to head to the bedroom & if you slide the TV cabinet down a bit you can add a tall plant to the wall area to make things a bit more interesting.

All of the above are good…the first one doesn’t dominate the room….but …it does unify the room…the third one is striking and dramatic…with more flare

I do think keeping the peninsula white ties in better with the white table and tv stand…but an accent wall is a good idea to add a splash of color ..to bring a little life and for contrast with all the neutrals

I really love the look of the rug in Beverly’s first photo against the gray floor.

I love shag rugs …they are wonderful for laying down on to do your daily stretches.. even to watch tv…but there are a few maintenance chores that will be needed…a rake, to keep it fluffy… and avoid flattening / compacting …good spot cleaner as yours is basically white… and the right vacuum attachment to clean them deeply..paying special attention to the area in front of the couch…but …we make a habit of removing our shoes and avoid placing it where there are traffic patterns…last but not least use the right spot remover… some of them leave a residue that will attract more soil..🤷🏻‍♀️…search for this one… it is amazing for cleaning upholstery also.. and surprisingly inexpensive

As to accent colors I always go to pale colors from nature… like aqua or pale lime green…even a pale sunset yellow…darker colors are striking as well but can have a negative effect in smaller spaces…

Nice choice on the rug! Works well with your space/furnishings/style. 👌🏼 And the comfy, cozy shags are wonderful. :)

imo, your vertical mirror is well-placed and adds some nice height, light, reflection, expansion in that spot.

You have a very good eye. Alternatively, a plant could work there, too. So, either way. It’s really a matter of personal preference. I’m not such a personal fan of mirrors in a bedoom; and from the Eastern Feng Shui perspective, it is not considered to be so desirable. But people have mirrors in bedrooms, and that is also a matter of personal preference.

The architectural design on that tv wall is fabulous. I agree that it’s very interesting in the lines. I think I would just leave it, though... no accent color. I don’t think it necessarily needs to be enhanced that way, and I also think with the combination of colors in your space, I’d just keep the wall(s) simple. That wall, as it is now, is really interesting enough; so in this case, less is more, imo. However, if you really want to do an accent wall there, I would agree with the idea of a light blue/aqua, possibly... Or alternatively, a light taupe. Best thing is to get some large sheets of paper or cardboard/oak tag and hang it up to see how a colored wall might look and feel. You can also order some paint samples from Samplize.com.

Very nice space. And you have great style!

I tried a couple of colors. I take back the blue... would be too much of a disconnect with the cabs, and also doesn’t help with warming up your space, overall.

A taupe type of color is better. Here I tried PPG Stonehenge Greige.

If you want a burst of some vibrant color, I think the right red or orange could be nice. Here I used PPG Glowing Firelight.

But again, I also really like the wall, as is. Simple, flows, and nothing to distract from the great lines.

If you still want to bring in more color, another way is with accessories - such as pillows, a vase on counter with flowers, etc. Any flowers you like.

or you could just display a vase in color(s) you like, etc.

You could put a piece of crystal on your coffee table.

ETA:

Would you add curtains to this space?

William the space is a bit schizo in style. White and gray on one side and vanilla and brown on the other. It would have been nice to have the colors run from one side to the other.

I should’ve mentioned that the kitchen will be remodeled soon. Quartz counter tops and dark grey cabs.

OK, always good to have complete info when trying to advise correctly.

I would think twice about dark gray cabinets. Gray is out of style.

What color cabs?? White with black hardware seems off to me

The creamy/white rug with black lines looks great in the grayish tinted room. While the walls already look good with this, you can add a bit of interest with them. Consider adding a textured wallpaper but don’t pick something that overdoes the interiors as that would disturb the calmness of the space.

If you do dark grey cabs, consider bringing in some wood with it, at least on your peninsula/island.