Perhaps if you included an image of the tile, you would get some feedback. To my mind, however, I would say NO to anything gray, especially considering the warm tone of the adjacent floor.

Do you have another suggestion of colour of tile? And size/shape

What about marble? With a soft grain it will play down the angular look of the floor.

I know you didn't ask but I would remove the shoe rack and coat hooks. Get a nicer rug of the correct size...smaller. Oval might fit better.

And some art.

I think dark gray and charcoal are more versatile than people give it credit for. And you can test out warmer tones if you're concerned about it clashing with your floors. Also a nice entry mat can tie the two different floors together. One question I have is what is the riser on the stairs. Is that wood and what do you plan to do with that? I think it might be weird to have all three colors and floor types competing in that small area.

No gray. You need tiles in this palette, ivory and gold/brown, to echo the floors and stairs:

Kings Star Ceramic Floor and Wall Tile, Beige · More Info

Here's a tile from Datile in a smaller pattern.

You might be able to find a wood-pattern ceramic tile that matches your hardwood. With a coordinating mat over it, this solution could work.

Flor.com has carpet tiles you can mix and match to create a floor mat; Choose Flor tiles that are indoor-outdoor. Or get a piece of industrial carpeting cut in a tweed of ivory and gold/brown to use as your floor mat.

Since you have a white door and white molding, then keep stair riser painted white.

Since you're spiffing things up, maybe a more attractive shoe shelf would help. I don't know if this would fit. It's from Wayfair. Shelves are 10" deep, which is probably not as deep as what you have.

Agree with lluvdark - I think a warm charcoal that looks like a natural slate would look good in the entry - tons of old houses by me have that look so I think of it as more classic than trendy