Looks like the carpet comes in 15 colors, which can be seen HERE Sorry, although I am copying the web page address, it won't take you to that type of rug. Summer Fog is the lightest gray tone - This is Magnolia Bud - Have you ordered the sofa yet? I see that the Pottery Barn sofas can be covered in many neutral fabrics. Perhaps there's another color that would work? PB sofas and fabrics

Frankly I would whitewash or paint the brick area the same color as the kitchen. With the white couch and the gray floor I would pick an Oriental-type rug which has some warm colors in it, similar to what aktillery posted. I think a blue rug will look cold and jute or sisal will show every stain, whereas a patterned rug in warm colors will make child and dog mistakes less prominent. You can use those colors for pillows and throws and other accessories for a coordinated look.

Before you go to the trouble of moving the cable hookup (simple, inexpensive fix with a long cord along the baseboards), please just try Beverly's suggestion for arranging the furniture. By simply trying the furniture in that new configuration, I think most of us are certain you'll agree how much better it would be. Then you'll see it would be worth the minimal trouble to move the TV. When it's arranged differently, you'll have a nice conversation area, with the proper place for a rug and a pathway from the door that won't be across your rug.

Ok. No problem. Just measure your space carefully and do a scale layout to see if the pieces you select will really fit properly. The room seems like there is a step down into it? Measure that. That is a spot you will need to watch for fall protection.