put in something that you can run out into neighboring rooms or vice versa. Dark wood would look good with the cabinets. Is that a 50's aqua range? Cool!

Getting rid of the tile is the only thing that will look right. Everything else is just a band-aid.

There's no reason you can put down a larger area rug to hide part of it.

I'd do bold peach/black accents (if that is the grout color) ... I'm not a fan of peach either but other than tearing out I'd say incorporate it..... you're challenged with some very different color schemes here... (white appliances, warm golden cabinetry, cool gray walls, dark gray counter... ps I <3 your dog :)

ok, I agree with mrk. or you could look at floating floor tiles?