A front load washer/dryer takes about 60" with door open and you obviously need space to stand in front of them. So if you could put them against the back wall of the 7'5" wall, you could put a folding rack on top of them and a hanging area next to them. I think your original idea would work fine as well.

What is your budget? Are you looking to gut or do you need suggestions for more moderately priced fixes? If you can't afford to gut and are going for a cosmetic facelift, I'd be sure to have the walls, cabinets, and counters the same color or as little contrast as possible. I'd ditch the island and potentially get a very narrow kitchen console type table with legs that is open underneath so you have some additional counterspace without the bulk of an island.

First thing to find out is if garage conversions are allowed. I wanted to convert my garage to an office space in my last home and found that it was not allowed. Our neighborhood required every house to have a 2 car garage. Actually - it required 2 covered parking spaces, but you needed the covered parking spaces to be set back 30' from the street - which was where my garage was located. If they are allowed you need to price the cost of the renovation and balance that against the cost of the house. Renovation is expensive, but being that this is your grandmother's home, you may be getting a good price that will offset the reno costs. There are 1000 things that can change the costs of your reno. The worst case I ever ran across was when one of my employees decided to remove a wall between their kitchen and living space. It was a 200 year old home and by the time they were done discovering issues they were down to the foundation and one outside wall. This kept it in the renovation space vs new build space and cut through a lot of red tape and allowed them to keep the original footprint and setbacks which had changed after the house was built, but their $30k reno turned out to be $300k. I have also known many people who have gone through renovations without any major issues. You will need to consult an architect/builder or design/build company to get an idea of what this will cost where you live. It is not all bad to play with ideas before presenting to an architect, but you will want to keep some things in mind. The wall that runs between the kitchen and living/dining space is most likely the major support wall for the home (notice how it runs from one end to the other. You may be able to open it up some, but removing it entirely will be a major, major expense. Moving plumbing is always expensive, if your house is on a slab, moving the plumbing means jack hammering out the slab. Leaving the kitchen where it is and just creating some openings with support posts would be a far less expensive endeavor. There may be many options that you have not even given a thought. A good designer will think of ways to make the house work for you and will know the pitfalls. Not saying this is a good design, but an example that I did in 10 minutes that is a completely different thought than you considered. You really need someone who is a pro who will take the time with you to discuss budget and the needs of your family and figure out the best plan for your home within your budget. Most of the time this means making some compromises and making something better without fulfilling all of our dreams or breaking the bank.

@shasta, unfortunaly can't do recessed light over the sink since it will cast the shadow overhead. @chispa, the cabinet is ok to open.