If you are thinking about stools at the island I'd run the island parallel to the stove wall. If you have the space, I'd put a counter height overhang instead of bar height. Making it parallel you don't take up the dining space with island seating space and it may get more use. I find bar heights awkward and don't care for the higher stools required. To each is own of course.
In our last home we had a bar height counter that backed into our dining area and we never ever used it, because we just sat at the table.
I also could see running the lower cabinets into the dining as a type of buffet. I've seen similar in some new builds we visited in our area although I guess they did use some uppers as well, but I think it could look fine without.
This shows how it runs along into kitchen
Q