The Mount Nesugata Ropeway climbs from near Izukyu-Shimoda Station to a hilltop lookout above town. From the top you can see Shimoda Bay, the port, Cape Suzaki, and the Pacific coastline that makes the southern Izu Peninsula feel so separate from inland Shizuoka.
It is not a long outing, but it is useful early in a visit. The view explains the town's geography in a way the streets do not.