Is your mind set on vinyl? I would recommend Porcelain Concrete Look Tile. The quality is so much better and looks may be just what you are looking for.

Here is a suggestion http://www.harveymaria.com/us

Many tile companies offer Luxury Vinyl Tile in stone or concrete lookalikes. Amtico has some nice products mimicking concrete, limestone, travertine, slate and marble. Armstrong, Mannington, and Shaw also have these types of vinyl tiles in various sizes.

Here's an illustration:

Check out Mannington Adura luxury vinyl, lots of choices

Not the OP obviously, but I love the Mannington concrete look that was posted above and wish I had used something like that in my kitchen. We used congoleum Duraceramic in our kitchen because we loved the warmth and softness of the product. Unfortunately I cannot recommend it because after 3 years it is already showing hairline cracks in the tiles. Plus our installer had a terrible time with the nongrouted (our preference) installation. I wish we had gotten sheet vinyl!

Agree with Patricia - Mannington Adura. They had multiple choices in the light colors you describe. It's been down for 2 years and we love it....mops with just water and looks fabulous.

I'm running in to the same problem. I'm trying to get away from the tile option in my kitchen remodel but it's hard finding a vinyl that isn't wood. Prosource flooring store has some wide selections and they do carry the above brands so I may check that out again. Menards has some click vinyl that you described that I may go with as well. I think the above picture is the same flooring that I may put in my kitchen. It's currently on sale for $1.99 a square foot. I do like the above pic Diana posted. I'm finding most vinyl is the peel and stick as well and I like this because of the click option.

Maybe Marmoleum? Lots of options for patterns and choices in the gray/white scheme.

I was about to suggest marmoleum/linoleum as a modern alternative.