That's because you're thinking about it totally backwards. Gray doesn't have an undertone. Gray is achromatic - gray is colorless. Thinking in terms of gray having an undertone is how you -- and many others these days -- get into the situation you describe. It isn't a matter of all the grays you've tried so far look too blue. Rather all the colors you've tried so far ARE blue. They belong squarely to the blue color family but it's hard to tell because they have been grayed down so far, so close to a true achromatic gray, that they look *just* gray. So, they aren't gray with a blue undertone, they are GRAYED BLUES. This category of colors, grayed down so much that it's hard to tell what color family they belong to, are known in the architectural paint industry as near neutrals and chromatic grays. You say that you want a "light gray with green undertones". From a color consultant perspective, that makes it easy to put my fingers on exactly the color you want. Instead of rounding up all the grays and trying to figure out which one has a mythical green undertone, I'd start looking at the colors that are already organized by color family in the paint store/fandeck. The green color family to be precise. And then I would find the green that is grayed to the degree you want and also the lightness that you want. It's far easier than you would think because the color order systems that all paint stores use, have already done the work for you. You just have to know to use the order systems. Yep, all the colors in the paint store racks are organized by color family. They're not organized by undertone because not all colors have undertones. Furthermore, manipulating undertones (of the colors that do have them) is what fine artists do on canvas. Undertones, unless it is a decorative finish, have no function in architectural paints. People find that hard to believe and it needs more explanation. Can't have an undertone without masstone. Undertone is what you see when you spread a color at different rates (or thicknesses). In other words, paint can be applied or spread anywhere from thick to thin. When it's spread thinly, that's when color undertone is revealed (if there is one). Fine artists apply their paints at different thicknesses to get multiple effects out of one color. In architectural paints, the manufacturer states optimal thickness. It's called spread rate. The intent is to spread the paint at one even thickness. Unlike fine artists on canvas, at no point is the paint manipulated on the substrate (the wall) to reveal undertone (if there is one). Architectural paints, with the exception of decorative finishes, do not utilize undertones. Rather, they revolve wholly and totally around masstone organized by color family.

Benjamin Moore Nantucket Gray.

I also love taupe, but getting one that is just borderline and doesn't go flat gray or pink or purple is tough and will also depend on the other colors in the room. I have 2 go to taupe paints that I try first and usually one works, but if not I know what direction I need to move. One can be purchased at Benjamin Moore - have them look up Devine Color Cappuccino and make you a sample. (Devine Color was bought out by Valspar/Sherwin Williams). I think this one is going to be darker than you want, but is that color that chameleons between gray and beige. The lighter version and the one that I think most closely resembles your photo is C2 Filament.

Definitely take a tile sample to the paint store, but after you pull some chips, look at the colors in natural light. They have LED or florescent lighting in paint stores that is unlikely to be similar to the light in your home. Also look at the chips on a piece of copier paper so you're not distracted by a background color. Then get samples from Samplize.com or from the paint store to view in the light in your house next to your floors and anything else the wall color will be next to. I also use Simply White for trim so I think it's a good trim color. Gray-blues are going to be cool colors, so try to lean warm when you're choosing. You might be better off just using Simply White like the rest of your house.