Most likely published in Asimov's or Fantasy & Science Fiction in the 80's or 90's. The woman lived alone in a cabin in the Northwest, I think, and went down to the beach when she saw the ship land there. She had a dog then. She dances with the alien, a humanoid with eyes like gold coins.
He leaves, years pass, dog dies and she gets another. She is ailing in her cabin. The alien returns, and she had just died. He leaves, and takes her dog with him.
I really liked that she was remembered by someone, and that her dog was not left alone.