About half-way between Mishima and Hakone, Yamanaka-jo was once a hilltop fort, built entirely of earth with a dry moat to repel invaders. These days it's a beautiful, relaxing park where you're surrounded only by trees, fresh air and birdsong and, in season, lavishly colorful flowers like azaleas and wisteria. It also commands a fine view of the surrounding hills and, on a clear day, of Mount Fuji.
If you don't have a car, the bus ride from Mishima Station (south exit, stand 5) takes about 30 minutes and costs ¥610.