IMO the only place for a DW is next to the sink so maybe asmaller fridge or a sink moved a bit to allow for the DW.. Kitchens are designed by inches so a to scale floor plan would be ahuge plus here . Do it on graph paper show every window, doorway where the doorways lead . Every measurement clearly marked . Then you post here in a comment in jpeg format. That is how you will get help . DO NOT start another post on this space everything to do with the kitchen is dealt with here in camments.

I can't tell from the way you drew this whether you could move the frig to the wall shared with the living room. As it is, it is choking off the space next to the sink and making it difficult for you to imagine putting a dishwasher there. You do need to post a better drawing, and pictures of how it looks now would also help people understand the space and make better suggestions.

You may find the cost of a dishwasher isn't much different than installing a 24 inch base cabinet, so think about that before you decide what to do. I don't know how long you're planning on being in this house but people take dishwashers for granted at this point, so you may have difficulty selling a house without one unless this is a one bedroom condo. People would find a remodeled kitchen without one puzzling.

You can use a tape measure and graph paper to provide an accurate floorplan. Do that and it'll allow for recommendations.

^Agree - your plan looks like there's plenty of room for an island but once you get accurate cab/counter depths in there - I think it's going to be a squeeze and that the space would be better without it (a free rolling kitchen cart can be helpful or maybe a short peninsula)

If your Kitchen is really only 9' deep (top-to-bottom in the drawing) or even 10'D, I do not think you have room for an island:

• If cabinets on both sides of Kitchen (12"D + 1" door on top wall = 13"): 27" deep stove + 42" aisle (minimum for a one person work aisle) + 39" deep island (deep enough that you won't constantly have to be careful not to knock things off on the other side & no seating) + 42" wide aisle + 25.5" deep counters on the other side of the island = 163" (13'7")
• If nothing on the top wall & seating at the island (along back): 27" deep stove + 42" aisle (minimum for a one person work aisle) + 42" deep island (if seats) + 44" wide aisle = 155" (12'11")
• If nothing on the top wall and no seating at the island: 27" deep stove + 42" aisle (minimum for a one person work aisle) + 39" deep island + 36" wide aisle = 144" (12'0")
• None of these scenarios will fit in a 9'D or 10'D Kitchen, even if you reduce the island to 27" (24"D cabinets + 1.5" counter overhang on both sides)

Can you put anything on the bottom wall next to the stove?

Is the yellow new or old? If new, the refrigerator will not work where you have it running into the yellow counters. (I'm assuming the yellow is your old Kitchen - but that's an assumption.)

There are a lot of questions/unknowns here -- as several others have stated, we need more information. Everyone is just guessing b/c there's not enough information.

FYI...if you have a basement under the Kitchen moving gas & plumbing isn't that difficult or expensive. However, if you're on a slab, then it can be expensive moving either of them more than a foot or so.

You'll get more useful/better help if you provide a fully-measured layout like the one below:

[See the "New to Kitchens? Read Me First!" thread for more information.]