I think it comes down to personal preference. I prefer hardwood for a foyer since it looks very rich and warm. It also is adjacent to the stairs which are also wood, so it is great for continuity.
Tile tends to be colder, not only in feel, but in look.

herringbone or just match it to to the adjacent rooms?

We just took down walls, remodeled kitchen to make open concept to living and dining rooms Installed dark hardwood floors. It is a split level so this is up 1 step from foyer. I would like to install same floor in foyer and family room ( possibly bathroom)which are on the 1st level and the foyer opens to all rooms. Does the hardwood need to run in the same direction as the living room ? (There is a large opening between the foyer and living room 1 step )

gary - do you have any pics of the "after"? I's sort of in the same dilemma and our foyers are similar

@jeannie b 

I wish we did more of it. It came out great.

@ gary A that looks fantastic! i like the border and the transition to the surrounding room, and that the other room doesnt have the same pattern. It really stands out. Is that LVP? Im trying to attach my before pic but Its not working, but. my current dilemma is what flooring to put in for the foyer because the family room (to the right) is hardwood, and we are not changing that. Also the kitchen isn't getting redone any time soon, so the entry flooring has to visually make sense with the current surrounding flooring. I'm leaning toward a non-wood look LVP

@jeannie b

It's white oak. If you decide on wood think long and hard about what type of poly. We used Loba and hate it. There's a lot of sun that comes into the house. You see faded spots. Can't put down area rugs or it fades around it. Everyone warned me to go with a solid oil based. Hindsight is 20/20ᾓ7ἿE‍♂️