RE: For and against driving on Rügen.
For: I have lasting mental images of Rügen from my trip there, and most were of the countryside. The searing colors of the green fields highlighted against the deep blue northern sky. The small little hamlets that look like something out of a Tolkien book. You won't be able to stop and linger at these small moments if you limit yourself to public transportation. Plus, public transit services mostly the towns on the island. As beautiful as the countryside is, I found several of the towns surprisingly ugly. Lots of Plattenbau from the DDR period and quite a bit of neglect. Even Sassnitz was a little rougher around the edges than I suspected. Binz, though, is beautiful.
Against: If your main goal is to visit Jasmund National Park, you don't really need a car. You can easily catch a bus from Sassnitz, and you can't drive to the main visitor center anyway (which provides easy access to a nice cliff and beach walk). It's only accessible by a shuttle bus from the outside of the park.
Also, driving in most of Germany could not be simpler, but Rügen probably isn't the place to familiarize yourself. I found directional roadsigns far less comprehensive here than is usual for Germany. And if there's a detour for road construction, you may find yourself needing to take the backroads, which can be very narrow and VERY rough.
