Trains from Bergen auf Rügen, Binz and Stralsund. A change may be necessary at Bergen or Leitzow if arriving on a long distance train. The train station and bus station are next to each other, and only a short walk to the town.
There is a bus link to/from the Ferry Port (for Sweden). If using the regular Sassnitz - Binz bus service for the ferry, the nearest stop is in Dubnitz (after the turning to the port, at the top of the hill, if traveling from the Binz direction). It will seem quite a long way from this stop to the terminal if you are backpacking!
Frequent buses to Binz and other Rügen towns. Beware that, on rural services, changing from one bus to another seems to be popular — the driver will announce "umsteigen (placename)".
Sassnitz: the harbor
The old part of the town behind the northeastern end of the harbor. The town is is on cliffs above the harbor, there are steps down near the shops, or it can be approached through the old town. Walk past the shops (the sea should be on your right) and fork right downhill.
Ferries to Sweden used to leave from the harbor here, but now use the modern port near Dubnitz known as "Fahrhafen Sassnitz".
Sassnitz harbor: the conning tower of HMS Otus is on the left-hand side
U-boot museum, near the disused ferry terminal. Perhaps surprisingly, the U-boat (submarine) on display is a former British submarine, H.M.S. Otus of the "Oberon" class, which was towed to Sassnitz after having been saved from a scrapyard in Portsmouth (GB).
Take a bus to Kap Arkona. A change of bus may be necessary in Altenkirken, although the driver may confuse passengers by simply changing the number of the bus they are on.
There is an extensive craft centre near the bus terminus in Putgarten. It is about 2 km walk to the Kap, where there is a lighthouse museum.
The cliffs at Kap Arkona
There is a supermarket along past the shops, turn to the left if you've come down through the pedestrian street from the train/bus stations.