It all depends on the stone. Sometimes the stone on the outside of the home is larger than what might be appropriate for the interior. They all need to play nice together. I personally like when the exterior stone is used n the inside. Makes a good statement about the home. I would use it on the fireplace, but I would rethink it for the face of the island. You might want to consider a different material like board and batten or shiplap.

I would use the exterior sone on the entry waal to look like a continuation of the stone and that and the fireplace I have no idea why you would use the stone anywhere on the island and BTW you do not need legs on the island for support of the overhang there are great invisible steel supports , IMO on the island will scratch your legs and honestly look silly there