Tokyo is the obvious excursion — just 30 minutes by express train — but since most visitors arrive from Tokyo the flow tends to go the other way. Yokohama works equally well as a base for exploring the capital without staying in it.
Kamakura is the single best day trip from Yokohama: a 40-minute ride on the JR Yokosuka Line brings you to this medieval capital filled with Zen temples, Shinto shrines, and the enormous outdoor Great Buddha (Kotoku-in). The Enoshima electric railway and nearby Enoshima island add another half-day's worth of exploring if the weather holds.
Hakone is roughly 90 minutes from Yokohama by the Romancecar express from Odawara (reachable via JR from Yokohama). The volcanic highland offers onsen, mountain scenery, views of Mount Fuji on clear days, and the open-air Hakone Museum of Art. The circular route — train up, ropeway and lake boat down — is a classic Japanese excursion.