Behr's Silver Tradition is a soft warm gray, that will complement both main colors of the rug. It looks beige in the can, but is a taupe gray on the wall. We've used it in the LR/DR, Kitchen and MBath. To add pop to the inside of the built in, why not mirror the inside back, or use a silvery wall paper for extra pattern? You can use gold tones too, because that beautiful rug has both. I'd also paint the exteriors the same as the wall color, unless there's some architectural feature you want to emphasize. It's going to be a lovely room!

If you want to use BM, you can match the Behr color there.

Beautiful rug! Is your plan to keep the trim and wainscotting white? If so, do you know the name of your current colour?
It looks like this room is fairly open to others. Is it important to you whether the colours flow? If you know the name of those colours, it would help us better guide you. A few more pictures would help too.

I definitely want to keep the trim and wainscoting white- it's a very open room. It opens to the hallway which is BM Silken Pine (light grayish green) and to the kitchen which is currently yellow but will also be painted.

This is your rug right?

That is the rug!!!

I see a deeper color on the walls. Here are some suggestions, including a few tans that pull out the accent color in the rug:

HI -- The rug is real nice . Don't do grey , it's getting to be overdone and I don't think you should match the rug . The rug should be a feature and if you match it , it will just be ordinary . I am going to shock you maybe , but I think you should do black in this dining room . Black is magic in a room ,especially a dining room. Then paint the inside of the china cabinet a real strong pretty color like a cobalt blue or another bright color or line with some metallic paper or metal leaf the interior .

Beautiful but I would pick up the blue for accent pieces.

I like lefty47 suggestion...very dramatic.
You might also paint the wall gray and for wall decor black matted prints with burnishedgold /bronze frames

Smashing chandelier under a glazed ceiling.

I would pain out the white cabinet.

Lefty47, would you paint both above and below the chair rail black? I think you would have to, because the black white contrast would be too stark? Black walls, black cabinet with mirrored interior, glass shelves and interior lights, and a crystal chandelier would be beautiful. And if not black, a deep purple, cobalt blue or bottle green.

I love BM Gray Owl. I have it in my house and it's a soothing color that goes with so much. Would look great with your rug. Hopefully you can see it okay I'm the picture.

HI -- Rachuba -- To answer the black wall being to harsh with the white wainscoting ..... No I do not believe this will be too stark or shocking and it could be any dark/near black color . The white could be creamed down if preferred but I think it would be stunning . I have seen it done with a dark navy and that was beautiful . And the black and white is very popular and timeless .

Any suggestions for a paint color one shade darker than the BM Gray Owl? We have a ton of natural light and it looks white on the dining room walls- looking for a little more contrast

BM Stonington Gray is a shade darker

I like Pratt & Lambert Armory

How about BM Gull Wing Grey and BM Steel Wool?

Or... If you are willing to go navy, how about BM Hale Navy and BM Eclipse?

And keep lower portion of the wall and trim white. Here's simply white.
Is your ceiling white?

I would use one of the lesser colors from the rug. On the back of the cabinet I would go with the gray.