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I'd put the sink on the island.
Can you put the fridge under the stair? That could buy you depth so you wouldn't need to buy a counter depth fridge.

I'd put the stove on the right wall if you can vent it outside from there.

The island location depends on dimensions. Generally they go about where your kitchen wall was.
I'd like to know a little bit more about your program and how you want to use your living room and dining room.

I agree that you should put the sink somewhere that the dishwasher should go next to it. Also, I'd prefer to have my sink in the island or in front of a window so I can see stuff when I'm washing diahes, etc.

So exciting! We are going through this now too. Have fun!

@SugarplumsMom: we are actually adding on to our house, the kitchen is just one piece of the puzzle, so we are hiring it out. We will be doing what we can ourselves, paintings, etc. as time allows.

@SugarplumsMom: Use underneath the stairs as a pantry!

I really like the idea of the stove on the island, especially if you don't need to vent it (not sure what the local codes are). I know a lot of people hate that, but if you can't move the sink, you don't end up with the triangulation idea and have everything all kind of right on top of each other. Then you can do a stepped island with a higher wall that faces the living area to hide the mess.

I'd put the sink under the little window and leave the island as a flat prep area. We had a stove/oven without venting (well, pathetic undermount venting) in our last apartment and hated it. You accidentally burn one thing and the whole room smells awful for ages.

I'd see if you could put the stove under the other window (note this really depends on your window and stove combo). That way you still have a triangle and something to look out at for the sink, stove and the prep area. Something like this: http://www.contractortalk.com/attachments/f11/122612d1418173390-stove-under-window-stove1.jpg

@SugarplumsMom: that actually looks decent, I mean, a designer could probably tweak it to make it more efficient. I wouldn't put the table so close to the island though, that doesn't quite make sense to me BUT it is how my SIL has it in her house in Europe.
Also, what about a stovetop and then two wall ovens? Does that give you more options?

@SugarplumsMom: the only thing I see missing is counters on the side of the fridge. So if you get a drink out, a place to set a glass and pour a drink without walking across the room.

@SugarplumsMom: I think you should go totally open concept if you can swing it. Or add a support beam hidden in the ceiling. We took down the wall between our kitchen and dining room and considered leaving part of it for a while and ultimately are really glad we took it down!

Your new layout looks great, any reason the island is t centered in the open space? Centered with the sink might be nice. Is that a support post?

Also we built our own "island" using IKEA base cabinets and put a piece of quartz on top, love it!!! I put it in quotes because we ended it up putting one edge of it against the wall, making it a peninsula? Haha. But after the wall was down we put a mockup in a few spots to make sure we'd have enough space to walk around and we have a door in our kitchen that we come in through 90% of the time so this felt better for us. We did all the construction ourselves though so we had time to move things around.

@SugarplumsMom: Anther idea just to balance things out would be to shift the island so its more centered in front of the sink and that gives you a bit more space by the fridge to run the counter. I also would consider putting the fridge closer to centered on the island

Could you forgot a wall oven for a range and put the fridge in that spot? It's too far from everything else.

I'd shift the island back into the main kitchen space and see if you could fit a table in the other side.

@SugarplumsMom: I love this. I'd tweak it by doing a built in banquette along the far left wall, that way you could shift the table over. Integrate the trim of the banquette to match cabinet trims. And the table wouldn't be hanging out in purgatory with chairs all around it (wasted space). Storage under the banquette seating. A bench on the other side of the dining room table so you wouldn't see tall back chairs poking up.