wikipedia has a good description of some scenery walkways:
Matsushima’s seaside attractions are within walking distance of the train station and ferry pier, but the best views are from mountaintops not so easy to reach on foot. The most spectacular views are from Saigyo Modoshi no Matsu Park, a ¥660 cab ride up from the station. It is covered with cherry blossoms in the spring, but the food available there is nothing special. Other overlooks are Sōkanzan, a promontory that juts out into the bay, and Ōgitani, a hill across the coastal highway from Sokanzan.