My recommendation to anyone spending two days on the Isle of Skye would be to just drive. Worry less about where you are going and just go. There are like three roads on the island, so you can't get lost, and regardless of where you drive, you are bound to find something truly beautiful.
I had a fairly humble bucket list upon moving to Edinburgh; I wanted to see the sites that inspired J.K. Rowling to write Harry Potter, learn to like whisky, visit the highlands. I have now been to every site even vaguely related to Harry Potter, I am an avid whisky drinker, and I went on one adventure with two of my very best friends in the Highlands of Scotland. More specifically, I went on an Isle of Skye camping trip that was one of the most stunning, exciting, and laughter-filled adventures of my many years of travel.