I think a fake hide will pull that area of the room together and will also tie in with the black floor lamp. Adding a table inbetween will also cozy up this sitting area.

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Where is the sofa?

Don't buy a rug to go with these two chairs. You need to get a sofa to know how big the rug should be. There's no way you need a rug for just two chairs.

I think that ottoman should be replace with a larger coffee table (round) and I wouls suggest a rug with a solid colour as to not compete with the patterned, bold chairs. (white/beige)

With it being a sun room, I would add whites and yellows and turquoise and would wait to see what other furniture you will be adding and then decide on the color and size of the rug and I wouldn't be afraid to mix paterns.

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