Allow at least 42 inches of clearance between the island and perimeter cabinets.

And more if you want to get by the stools when working. In the 12'9" space you could only go with a 60" island in same direction as in pic and it could be 48" wide including a 12" overhang for stools but you could only have 3 stools max and they would have to be small and with swivel to keep them from getting in the way of the fridge and not feel cramped. The only way I can see to get 4 stools would be to make the island a square with overhang on side by fridge and on side on end at bottom of page which I think would look okay because your kitchen is close to square shape.That would keep the stools away for the busiest work areas and give you nice spacing for people to walk around or cook with you. Sort of like this picture That would give you space for 30"cabinet under island with drawers across from the sink and 12" overhang on the 2 sides with the stools. Hope that makes sense