After trying multiple grey samples in my daughter's house, BM Stonington Grey turned out to be the right grey. She used it in the living room dining room and hallway. Those areas each have different lighting and Stonington looks good in each area. No blue, purple or green undertones that are noticeable.
Good luck. I once had to have a room repainted 3 times to get the right color.

I'm a huge fan of BM Weimaraner (an Aura color), it's on the slightly greenish/lavender end of the gray spectrum, no blue cast in it at all, and looks stunning with all shades of white.

Stonington Gray is on most of our walls on the first floor. I agree with badgergal - no undertones in any of the rooms, just a nice, true grey. It's not very saturated, though. I also like the next darker one up on the paint deck, Coventry Gray, but haven't used it yet. It'll probably go on the upstairs hallway when we get around to painting it.

We painted our family room, kitchen & laundry room BM La Paloma Gray & love it. It is a medium true gray. It was suggested to us. I was hesitant when I saw it in a color fan, thinking I wanted something lighter. We do have a good bit of sunlight.

Our dining room is Coventry Gray. I chose it because I wanted light blue. It is definitely very, very blue. So avoid that one.

My bedroom and sitting area are Gray Owl. It is very soft, almost "watery" warm gray. Not much saturation, no blue. I have used it elsewhere when I want a neutral, warm light gray.

Revere Pewter is tricky when looking at a fan deck or sample card. When you get it up on a wall, though, it almost always just reads "warm gray" with few undertone problems. It is a great default gray--I've NEVER seen it look bad.(I have that one in a stairwell.) It can look very dark in a north room, but it sounds like they have plenty of light.

Very helpful thread, thank you all very much! I'm smart and ethical enough to know that one must not choose pets on the basis of color, but I really love that Weimaraner color, so perhaps that is the right grey for me!

Thanks for your help. The stonington recommendations got me on the right path. We loved it and were going to select it because it looked great on the walls. But then when I turned around to face the windows, I realized it was the exact color of the stone churches and buildings across the street. The walls really needed more contrast to what is outside the windows, so we went one step darker with the conventry grey and it is fantastic. Great recommendations.