Personally, I don't think the gray paint compliments the floor very well.

Nope

Not really as you have 2 different flooring in the entryway. Travertine Is a hard one to match as everyone sees a different color tone in it. Color wise not sure here as you have allot of colors here in the area. Do you want to enhance the tile or railing, or the darker color tile by door? I would not go the blueish color, maybe a more tannish light color?

Ken

I had travertine in my last home. I was able to get the following colors to work with them. BM Thunder, BM Berber White, Valspar Lambs ear (matched to BM).

First off, travertine tends to have a pink beige undertone. Here's what Vancouver colour expert Maria Killam would recommend for a greige. She defines greige as a very pale neutral that looks like grey and beige combined:

"BM Pale Oak or BM Cedar Key: The most popular greiges for updating pink beige flooring or to relate to existing taupe finishes. Choose the correct greige if you have existing pink beige or taupe hard finishes. Cedar Key is slightly more pink than Pale Oak so move them both around to decide which one looks the best."

I tried cedar key and pale oak as well. If you want less beige and more grey that works, try lambs ear. Berber white worked well in a bath that had no windows. Thunder is a griege that leans purple, but worked.

Cedar key has a strong pinky beige tone. You want some variation.

Thunder looks like it's too dark, I think the Berber White looks very nice (but it is really a beige ). Pale oak looks like it could work. When I googled the colors, they also showed Classic Gray which looked a lot more like a greige that you might like. Not too dark.

Cedar Key looks very good. Light enough and not throwing too much color.

I think all it needs is a darker shade of white.

Current white seems too stark for your wooden door and balustrade.

Should I use a different color in the entryway than the hallway? I've thought about using a taupe for the entryway. There's some orange in the slate floor that's similar to the orange in the door stain.

That was such a good video @User!

I bought Maria Killam's 2 ebooks, read those, bought paint samples, and decided to go with SW Creamy. Maybe a darker color would be better because those are both darker areas, but I didn't like any of the greiges or beiges neutral enough to go with both (I'm not a fan of browns and tans in general). A cream that I do like seems preferable overall to a more ideal color I don't really like.

SW Creamy looks like a great color.