Would any of the other sizes of this rug work in there? I have a 5x7 in my kitchen, love it. If not, I’d go with what works best for your comfort. :) (I think I see the ocean beyond? Great view!)

I have a ruggable runner in front of my kitchen sink. I strongly recommend it for the kitchen - easy to vacuum for everyday cleaning as well as put in the washer and dryer to get it really clean. It comes out of the dryer looking as good as new. In front of the stove, I have one of the cushy mats (not ruggable) - easy to wipe off grease and stuff.

Or even placing a rectangular rug between the sink and island would work great. Of course it wouldn’t fit perfectly, but sometimes that’s what a kitchen calls for; embrace the unordinary!

I’m jealous of the beautiful space you have. All those windows are great. My suggestion would be to make a dinette area on the wall where the tv is currently. To furnish it I would use an upholstered bench along the wall flanked by two small bookcases. Find a narrow table to use with a couple of side chairs opposite the bench. I would keep the sofa where is is but pull it out from windows by about a foot. Try sliding the chair to opposite end of the sofa so that it faces the windows. Get a beautiful tv cabinet (keep it low) and place it with the tv in the area that the cafe table is currently. The tv will block the window slightly but will will be unobtrusive in that corner. Shades will be a must if you plan to watch tv without glare during the day. Plus will help with cooling the room in summer and make it more comfortable to use that space. I would use small recessed lighting above the dining area. A couple that shine down on table and one the could shine on a pice of artwork above the bench. I’m also a believer in dimmer switches as I like to dim lights at night for mood lighting. I would also use floor lamps to flank the sofa. I would suggest tripod style lamps as they make a great transitional look. Add a rug and you’ll have a wonderful room.