Right now, the permanent surfaces in the rooms are so neutral that you can go in any color direction.

You need an inspiration piece from which you can draw the colors. It can be a picture from houzz, a piece of fabric, a plate, a piece or art, a view outside, anything. But some anchor which will help you define the color scheme. You might also look at design seeds for inspiration. Awhile back there were a number of threads on using design seeds to inspire a room. You might find perusing those threads helpful.

You can go to houzz and search on turquoise island in kitchens. If you find one you like, then go look at the entire project to see how they decorated the nearby rooms. That might give you an idea.

There are many shades of turquoise. You can go to Ben Moore or Sherwin Wms on line and look at the color gallery at shades of turquoise. If you select one, it will pop up with some other colors that coordinate well.

If there is a natural break between the dining room and the living room, I'd consider breaking the color there to help define the separate spaces...make them coordinate but define them as separate rooms.

Do you like gray? I notice it is in your BS and fireplace. It would look nice with your white cabinets and contrast nicely with the beige furniture and wood floors/ trim but still be considered a neutral. You could even use various shades on the same strip for depth and interest. Then you can bring in color with art, pillows, etc.

Your backsplash is gorgeous. I can't wait to see it installed. What about a grayish blue for the walls?

Check out SW Agreeable Gray or Accessible Beige, or BM Edgecomb Grey.

Just had to say that I think those chairs are really neat!

Adding to the paint names above ... BM Grant Beige would go well with the main/fixed elements in the space.

BM Duxbury Gray or Carolina Gull might pick up the dark colors in the marble and fireplace. BM has some nice combos of other colors to mix with those two grays. What color are your perimeter counters? I don't think you have to give up your idea of a fun color for the island--just pick it carefully.

Besides turquoise, what's your favorite color?

i'm no good with color but grey does sound nice. I have to add that those chairs are awesome!

That backsplash is so pretty

I echo what mayflowers just said.

I also agree with mayflowers suggestions.

Here's how it might work. Pick an inspiration...in this case the fabric...which works with a turquoise island. From the fabric pick a wall color, a ceiling color and the turquoise you want for the island. You can then use the colors in the rest of the palette to bring all your rooms together...maybe use the lighter palette in the LR, the medium colors in the dining area...keep the chairs in the yellow green tones and maybe select the gold tone or the deeper taupe to use on the pew fabric. I'd use the same fabric for the drapes in the dining area as I did in the kitchen. I'd select a more formal fabric though for the LR. I'd probably pick the soft beige for the LR walls. If you don't like this fabric or this color way, that's ok...it's just an example of how this could work for you.

Here is a selection of fabrics that would coordinate with the inspiration fabric. These could also help inspire wall colors for the rooms. All the fabrics are from calico corners only because I find their web site easy to use.

Using this color palette, for example, you could emphasize more of the brown tones in the LR and more of the green tones in the DR. This way, the whole large space will coordinate nicely, but your space will feel larger as, with color, you are defining 3 distinct areas.

That softer color palette is better than what I picture when I hear turquoise. Turquoise to me is the deepest of the blue green family. Pretty fabrics, Annie.