Provide a photo of the area currently showing the sofa, coffee table & chairs from a different angle. I see no need to have something plain selected for the area rug. There are area rugs that can bridge the gap between your leather sofa and patterned chairs.

I have a low pile Mohawk carpet with a subtle pattern cut to a 9 X 12 area rug in my living room. It is wearing like iron. This is a room we spend a lot of time in. Take some pictures of the room to a carpet store. Look at their remnants first as they will be the least expensive option. If none of them look right, move on to their stock carpet and then to the special order items. Mine was a special order, but not inordinately expensive. Be sure to bring home samples before committing because colors don't look the same at home as they do in showrooms. And as Beverly said, there may also be off the shelf 9 X 12 area rugs that would work. Just because the chairs are patterned doesn't mean the rug also can't have some pattern. If there is a good salesperson at the carpet store they can be a lot of help.

If you want to try a rug you find online, order the smallest size to see the colors in person and be able to return it more easily (for less money - no extra shipping charges) if you don't like it.

I would choose a Deep Rich Blue to ground your space.

The trellis frames are a little precious. a lamp on the built in would add interest. something darker to add interest

Great room. You have a good eye. I think your idea of light beige with texture or pattern is spot on. I'd go with a slightly more contemporary pattern to off set the other traditional pieces in the room. The contrast would be great.

IMO a blue rug would be great I agree those trellis pieces are a bit blahmaybe some interesting art then choose a color from it I would not do beige .

Included here are some rug ideas for you that could work wonderfully with what you already have. Please take a minute to look and see if anything calls to you.

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The last one above would look great. Something that has a woven sisal look would add interest to your room. Just my opinion! your home is lovely!