For my proposal I decided to keep the seating at the window to take advantage of the bay window and view. It seems like the right thing for the space in general and the logical place. I placed a large banquette up against the bay with a table and chairs tucked alongside. This will eliminate the traffic flow around the outside edge and improve space for circulation. I think the seat also promotes the idea of lounging in the area and enjoying the space.
Since you were open to locating the table in the Family Room, I figured rather to bump the peninsula slightly into the room to provide more circulation in the Kitchen. I think this will be less intrusive than a table and again seems like a natural location, as it will provide a view into the room for anyone at the sink and the bar provides a slight separation without having a solid wall.
The big problem with the existing plan to me is the 2 doors chopping up available wall space, making it difficult to develop efficient and adequate spaces for all the appliance and storage needs.
So I added a new interior wall on an angle matching the bay which relocates the dining entry along a vestibule which could also provide space for a walk-in pantry. The resulting plan provides wider wall spaces for the work area, and essentially eliminates one door by combining the 2 into a single doorway. This also has the effect of limiting direct views and sound into the kitchen from the dining which might be better for formal dinner parties.
The plan takes advantage of the angle to enhance views throughout, and a new island in the center now has plenty of space for circulation, plus forms an edge to the work area. I placed tall items like the wall ovens and refrigerator at the ends, with a wide counter for the range against the wall so you can have a proper hood. This provides a nice opportunity for a dramatic mosaic tile wall.
I utilized the pocket of space resulting in the corner at the peninsula formed by the refrigerator to tuck in some cabinets that could provide space to store away counter top appliances. You could also if desired switch the wall ovens and refrigerator if it made more sense for your use.
I rendered the cabinets in an off white with light grey stone (or quartz) counters. I wasn’t certain of the exact ceiling height, so am showing a soffit above 42” upper cabinets. If more ceiling height is available you could have additional upper cabinets above or just open space.