What still puzzles me about this stair is that given a 9ft. ceiling height and 7 3/4"+ risers, the thickness of the second floor (ceiling to finish flooring) would be over 16" if there were 16 risers and it would be about 8" if there were 15 risers. For the smaller floor thickness the floor joists could not be larger than 2x8's and for the larger floor thickness the floor joists would be about 14" Since a typical floor thickness is about 12" I am greatly puzzled about your stair construction. Is there something unusual about the floor joists at the second floor? Is the ceiling height 9 ft. plus a tray or coffer? To accurately define the stair riser height you should give us the floor to floor height and the number of risers. To increase the distance from the front door to the stair by turning it, you must put one more riser at the lower run which would extend it farther into the lobby. If this doesn't make sense to you, you should ask your designer to draw the two conditions to scale before telling the builder to modify the stair. I could draw it if I knew all of the dimensions of the existing conditions but what you have posted doesn't seem to add up.

If you want an entry area, put up a wall and have one. We have a home now where someone knocked out the wall between the nice entry and the living room and we basically put the wall back with a shoe bench and shelf arrangement (freestanding because we didn’t want to do construction work) because it just flows better that way. We also just looked at another house which we decided not to go for after much deliberation in part because if we opened it up to get much needed space, we’d end up with a big box with the front door entering right into everything, like a small apartment layout. Houses, especially houses with kids and lots of visitors, need some way to control the flow of traffic and direct people to where they should take off coats and boots and what have you. If you have room for a mud room, great, but if not - entry area is a necessity, IMO. And people are going to be beyond bored with HGTV style everything probably sooner rather than later - next year or the year after it’ll be some other designer and they will be putting walls up because everyone is sick of open plan and always being on display while cooking. If this is your forever home then do what you like and what feels good to you, not what’s popular on HGTV. (If you were going to flip the house then I might be saying something different.) Personally, if my front door were that close to my kitchen, I’d really really really want some kind of wall for privacy. Who wants all your mid-meal cooking mess to be on display to anyone who comes to the door?

and nothing in the hallway? I do feel I need the foot trafficked areas to have rugs to protect my floors. I like the idea of a wider rug in the entry area, but I still want a runner in the hall. I guess I’m just lost on how to approach mixing and matching rugs in a contiguous area.

If you go with tile, I like #3. You can do a darker grout so you don't see the lines as much. But you also say that you're sanding and restaining all your hardwoods as part of your remodel; can you lay wood in your entry? From just seeing the one picture of your entry, I think extending the wood would look really nice. What does the flooring look like on the other side? Can you stand at your front door and take a pic?