is it vinyl or tile?

It is a great looking floor. if mine, I would paint the walls a light creamy greige, replace the ceiling fixture, new artwork and replace the rug with a rectangle.

Suggest luxury vinyl tiles in a natural stone look and also works with the carpet. I think its feel will provide a seamless transition to other rooms, while feeling inviting and updated.

If possible, suggest painting the foyer a warm, neutral to lighten the space (only select a color after flooring is installed and have tested a few). Instead of a round mat, consider a runner (safer/nicer) with similar (but muted) shades to create a connection with the living room.

Why do you want to replace it? What you have looks great, and seems to fit the bill based on your description of what you want.

Other ideas, as I find there is usually a trigger effect. At some point consider painting the inside/outside of your door a softer shade and update the light. Look to connect everything, no matter what you decide to do.

Many thanks to all responders for your thoughtful messages. I am proceeding with a natural looking stone tile in a soft beige color that goes with the walls that were recently painted. I hope to post an after picture when completed if I remember to do so.

Sorry that choice will be a nightmare for those that come after or if you choose to swap it out...tile is not easy to be rid of.

Slate is often a good choice in an entry. Your current tiles seem too light for the foyer and the yellow gold walls don't seem to work with anything so I'd advise you repaint the foyer.

It appears to be a traditional style home and I'm not sure how the fireplace stone selection fits with anything in the home.

A classic approach to your foyer would be some type of two color square tile/stone flooring

Flooring on the diagonal would make the space appear larger.