If you are having a dining room, and this seems to be an open-concept design, then you probably don't want doors. If it's to be a music room, as in for practice, you probably need some doors.

Can we see how the house looked before? What is the age of the house?

I would do all one flooring in the living room and kitchen

I suggest you think about how you want to use the spaces and if you think you need doors there. There are a lot of things I see in the plan that I would not recommend doing, but I assume your designer has knowledge of your need and existing conditions of the structure that I am not privy to and can justify everything in the plan.

Budget permitting, do the same flooring throughout the kitchen and living room;

if not, extend your tile at least to the far edge of the island.

If this seems awkward, you might consider adding another base cabinet beside your refrigerator and make it extend enough for its edge to be even with the far edge of the island -- you wouldn't need to add a wall above the countertop level to do that.

Alternately, you could just setting a wheeled table or rolling cart beside your refrigerator on that tiled corner to claim that corner as part of your kitchen -- with wheels so you could roll it outside when you have a family BBQ.

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No doors. No tile in kitchen. Can I ask why you would want to put tile in kitchen? Is that some regional thing? Kind of bitter as I just finished ripping out a tile kitchen.

In my area, it is never done and hasn't been for 15 years (well occasionally in custom homes).

Tile is rough on feet/knees/back and glassware/porcelain etc. Grout is not fun to clean.

Now I have a beach house that is a rental that I tiled the main floor. Biggest regret of the house. Can you see I have strong opinions?

Open concept = single flooring type.

You need to cross post this plan in the Kitchen Forum. You've got some issues that need to be addressed. That stove and lack of counter space on each side is just the start. Let the experts take a look at the kitchen design. It needs attention.

"Open concept = single flooring type."

I agree with this and I disagree with this. It all depends upon how the one open space is designed.

With four functions (kitchen, dining, living, and circulation) in one large space it sometimes helps to define those spaces within the larger space; through the use of material, ceiling height, wall openings, and furniture placement. Many of the time defining the four spaces limits the flexibility of the one large space.

The plan in question appears to have been designed as one large space without thought of furniture arrangement or circulation paths to make one's experience of the space pleasant or have any coherency.

My in laws used to have a place where the previous owner converted a garage into living space, but it was directly adjacent to the kitchen and made a very generous kitchen with eat in dining area. There was also a formal dining room but it was next to the kitchen. In your plan the piano room seems so far away from the kitchen that especially with doors it is hard to imagine as a dining room. I personally like the idea in your plan as is of having a piano room with doors you can close off. It could be a library, a study, a second hang out place besides the living room. My current home is not open concept and with 3 young children I actually like it that way because it gives each space a function and helps me with organizing. We have a music room with instruments and toddler toys in bins for the 1 year old. It is cozy and I like having my coffee on the loveseat reading books with my kids. We have a separate study with industrial baby gate where my husband and I can do work and our 6 year old can do crafts. I am grateful to have both of these individual spaces on my main floor and it is also nice when we have overnight guests so people are not all on top of each other in the great room for the duration of the visit.

"we are redoing the whole first level"
Then presumably other things can change?
How do you plan on furnishing the living room? The kitchen is poorly designed.

"doors between the... (dining room) and the front hall?"
No, I wouldn't, were I you, but I'd change the swing of the entrance door.

"I'm not sure if the tile should line up with the fridge or the island."
With the island, assuming you go with that layout, and assuming you tile.

A couple of thoughts upon seeing the plan and reading the comments:

--Does your local jurisdiction and zoning ordinance require covered parking space(s)? If so, this will make your house nonconforming...;

--Given the lack of spatial definition in the kitchen/living areas, it would probably make most sense to make all of the flooring in these areas the same. Wood flooring, for example, would be a good choice, but that means immediate clean-up of water/liquid spills in the kitchen. Tile is another option for both spaces, but it's a hard material on the feet and legs, plus large tile areas can get very "busy" with all of the grout lines.

Good luck on your project!

I'm still a little confused about whether you will still have a piano in there if it's a dining room. I don't know about the practicality, but if possible I would consider double pocket doors. That way you can have the full double opening if you have guests circulating in and out for dinners / parties, but can have sound dampening / privacy if needed.

To be honest I'm not liking the location and the path to the room as a dining room. Since it is further away and not convenient for every day eating it seems like it would be a formal dining room and just used occasionally (not exactly helping a space issue). Is that what you'd envisioned? If so do you really want guests walking through the mudroom?

What in your current house are you lacking and what do you want to improve on with this remodel? Where are you lacking space and what are you lacking space for.

In the plan shown the kitchen looks to me like it needs a lot of help and as others suggested posting it on the kitchen forum would be a good start.

Then I'd also go through and consider how you're planning on arranging furniture and use the areas in the living room. Were you planning on having a table there for eating too and then living room furniture. Based on the shape that seems like it would work best that way, but then doing a dining room too seems like too much space devoted to eating spaces. Island, next to kitchen, and then also a dining room.

I would take a look at what you really need and want and then see how this space works for you with that. Maybe you'll need some changes.

Mark, that's only acceptable at music conservatories. When I was in college, I was friends with two piano students who shared a small duplex. The parents of one of them bought her a baby grand piano that just fit their living room. I don't remember how they got it in, because there was no room to spare. Certainly no room for a dining table, or any other furniture.