Lovely space. You should think if you and your family living style would prefer an open kitchen or a closed one first. Many people do prefer closing the door to the kitchen when entertaining. Once you've decided that, then saving or removing the cabinets is obvious. I would also look to a modern, sleek appearance for the cabinets. In keeping with the style, a slab door in a veneer would be nice. Maybe as you have so much of the stained wood look, maybe you lighten the kitchen cabinets with a grey veneer or something in the taupe family, which keeps you in the warm range, but doesn't add more of the same to the space. Good Luck with your remodel project.

Remove it and the cabinet beneath it. Let the KD decide how to deal with that space.

Since it looks like you can expand your kitchen toward the island area, I would remove the bar and cabinet so the end of your kitchen is open to the family room. If you don't want it completely open, you could build in open shelving between those areas, which is very MCM.