How about a dark charcoal gray & off white rug with a big bold design pattern? {not a black one}. Then you could add pops of color with a bold color vase or artwork.I think a medium blue color would also look good with you walls & dark wood color. I see blue light coming in the windows in your photo & like it with the wall color.

I have 3 rugs in my house made by 'Momini' {not sure if I spelled that right, they have some great wool modern area rugs, & also traditional ones. My taste is more modern. Your walls are pretty neutral you could also do other colors for a rug such as purple, burgundy, green, blue etc. I would do those in more muted tones because your walls are neutral but still kind of bold/bright. It all depends what your personal taste is, is it more earthy & natural, or more bright & fun? Just go with that you like & trust your gut.