Based on your photo I'd probably do a wide runner from the door. But, I'd also consider how it looks from other areas of the house. If you can always see the hallway from a certain room and a runner would bug you because it would look off-kilter from there, consider that as well.

I would just put a rectangular rug in the area between the foot of the stairs and the French doors and leave the rest alone. Don't worry about the curve on the staircase wall.

Sabrina - would you run the rug lengthwise or widthwise there? If lengthwise, is it OK that the rug won't line up with the French doors?

I would get the largest rug you can find for the entry door

One rug at the door no need for little rugs at every doorway

The issue is your register. It can't be covered up so a long runner as wide as will fit between where the register begins and balanced to the other side of the door.

You can take the guess work out, with a drawing of the floor, and all feet/inches noted: )

Upload it as a jpeg, bold and legible in a comment box and use feet and inches for the lazy among us.

@clueless, You follow the dimensions of the area. So, long side of rug with longest walls.

So, something like this?

Lyn Nielsen - the quality of rug I will have right inside the door is markedly different than the quality I will have further in. We have some seriously mucky weather here - lots of snow, then melt with mud - so anything I put right inside the door has to be super durable and ok to get FILTHY.

No, i meant this:

Thank you, Sabrina! That's exactly what I was thinking but both my husband and mom thought that would look weird - like we were creating a living space in the foyer.

You could add a bench on the staircase wall to pull it together, IMO.

Oops, I should have added - would you do a larger rug at the door? Could it be turned lengthwise?

No. If anything, make the mat wider, but leave the current depth.

I like your idea of making a living space in the foyer. With the rug placement as suggested in red by @Sabrina. And with her idea of an {upholstered} bench/settee, you have an outlet there for a floor lamp or little table and lamp. Hang artwork there.

For the doormat, nothing interfering with the stair landing area (you don't want a trip hazard coming down off last step), or foot traffic coming from the parlor opposite.

Before I worried about the rug, I'd eliminate all the orange trim and woodwork. I'd paint that out. It doesn't work with the flooring in the foyer.