Andrew:
Shiskine is a wonderfully scenic part of the island, and a relatively easy walk with one very fun climb up and down a set of the course's unique par 3s -- the up-and-over, blind Crow's Nest, and, from on high, the drop-shot of the Shelf. If you're on the island, it's well-worth playing -- it's the best of the island's courses, very linksy, several blind shots, 12 holes, terrific scenery.
John, your comments on Corrie bring back great memories on my round there. I played late in the day on a summer evening, found the small clubhouse locked up, tried to pay the small greens fee in the honor box, found that locked up, and went to play my round, and had the course to myself. The picture posted does not do justice the majesty of walking that course, with Goat Fell (that's the big peak in the middle) looming over everything. Quirkier in some respects than Shiskine, I remember distinctly one green that was carved into the side of a hill, and I utilized the back side for a bank shot to get closer to the pin. I can't imagine anyone playing a round at either course and not enjoying themselves.
Andrew -- each of the small towns has a range of B&Bs and small hotels, and I believe the main port of Brodick (where the ferries come in) has a tourism office that could offer recommendations. There's a nice castle on the island, too, that's worth exploring, near Brodick.