Benjamin Moore Paper White. We also have gray cabinets and this is the color we chose.

You don't bring home 10 cans of samples. You use the paint chips as your starting point. What type of white are you looking for? All whites are a tint (very light version) of a primary hue, so are you wanting a yellow/red/blue/green/orange/purple tinted white? What orientation is your room--north/south/east/west? What is on the floor and what color--tile/wood/carpet? What is outside the windows--green trees/another building/a blue pool? All of these factors will affect the appearance of the color you paint the walls. You could start with some of the most popular whites--I use Benjamin Moore paint and would recommend White Dove, Cotton Balls, Chantilly Lace, Simply White, Decorator White, Linen White, Ivory Cloud and Ivory White. See if you can get a large paper sample from the paint store (they are available to designers and I'm sure the paint store can order them for you) and narrow it down to 2 or 3. Then get a very small paint can of the 2 or 3 you like best and paint a large piece of poster board with 2 coats of paint. Then view the results in your room at different times of day and evening on the 4 walls. If you still can't decide, consider hiring a color consultant for an hour or two to help you.

Combining emerald green and gray is tricky, and then it also appears you have beige carpet, golden beige shades and yellows in the rug. I think you can make the rooms work if you paint all the walls a neutral white - White Dove was a good suggestion. First, remove all your extra colored pillows and the rug so you are looking at the room with just the two main colors you need to coordinate with (the sofas). Put your extra green pillows on the gray sofa. Maybe you can use your gray/yellow rug under the dining table instead. I would replace the mirror on the dining room wall with large artwork that brings in the deep greens of the sofa to help coordinate the rooms.

on the wall with the arched mirror, opposite It, is a very nice color. It seems to go very well with your cabinets. I would continue that color into your kitchen.