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Should have mentioned...table would likely stay round. But could open to oval if we have an extension.

Missed one

I'd move it so it is centered with the island and fireplace. A round table might work quite well in your space.

agree with Sammie J

You don’t think there’s too much space by the door when it’s in the middle?

How much passage space do you need? The hallway, this walk through is here

first thing I noted was the wonderful view out all the glass. The fixture doesn't do much . i would swap it for either a ceiling mount or "close to ceiling' and the table adjusting based on your needs...a few inches forward...or a few inches back, is much easier. I removed a low fixture for a "close to ceiling' piece which purposely serves lighting needs [ on dimmer too] but blends in so if table gets skooched depending on season , and if more people are showing up, the fixture is not a problem. We have four distinct seasons and a patio door facing out right there to West to Southwest. Utterly hot w glare in the summer so table moves back a bit and assists w traffic flow. In winter...no entry /exit, and sun is low so table gets skooched toward glass a bit more along with plants on stands. I'd get rid of the fixture/ tons of ceiling mounts to assist with use of the beautiful seating area and do whatever you want to do w table/chairs.

I think a round table centered under the light works. My setup is very similar but instead of a door, I have windows.

I like it centered under the current light position. That way you can still see that lovely fireplace and there is more walking room in the major pathway from the family room to the kitchen. It seems to me like there is still room to get to the doors behind the table without moving it.

Of course, you are in the space and know how it feels. If you move it out, maybe not go so far as to line up with island??

I like it centered with the island - assuming that gives enough space from the wall. I’d prefer a bit more space by the door for a mat and people
Coming in and out. I love the idea of a round table for your space.